Avdhut explains in Guru Sannidhyan the genesis of Zero. He describes the concept of zero is one of the most fundamental and revolutionary discoveries in the history of mathematics. In this comprehensive exploration, we delve deep into the annals of ancient India's mathematical heritage to uncover the origins of zero.
From the Vedic period to the classical era, we traverse through millennia of intellectual inquiry and mathematical innovation, shedding light on the pivotal role played by ancient Indian mathematicians in the discovery and development of zero. Through meticulous examination of ancient texts, archaeological evidence, and historical accounts, this article aims to provide a comprehensive understanding of the genesis of zero in the context of India's rich mathematical tradition.
Zero—a seemingly simple yet profoundly transformative concept that permeates every facet of modern mathematics and science. Its discovery represents a milestone in human intellectual evolution, revolutionizing numerical notation, arithmetic, and algebra. While zero is ubiquitous in contemporary mathematics, its origins are shrouded in antiquity, with ancient India emerging as the cradle of this revolutionary concept. In this expansive inquiry, we embark on a journey through time and space to unravel the mysteries of zero's discovery by ancient India.
The Vedic Foundations:
The roots of India's mathematical heritage can be traced back to the Vedic period, spanning roughly from 1500 to 500 BCE. Amidst hymns and rituals, the Vedas—the sacred scriptures of India—reveal glimpses of mathematical thought and numerical symbolism. In the Rigveda, for instance, references to counting, enumeration, and geometric concepts provide early indications of mathematical inquiry among the ancient seers.
The Emergence of Numerical Notation:
As India transitioned from the Vedic to the classical period, mathematical thought began to crystallize, laying the groundwork for the formalization of numerical notation. The Brahmi numerals, dating back to the 3rd century BCE, represent an early attempt to systematize numerical symbols. These symbols, although lacking a distinct representation for zero, demonstrate the evolution of mathematical abstraction and symbolic representation.
Panchanan Mongal, Chandi Mongal, and Annada Mongal. Three Mathematical systems are described in a poetic form. Panchanan Mongal is basically on Beej Ganit. Seeds of Mathematics. Nowadays people call it Algebra. Chandi Mongal is for Geometry and Annada Mongal is based on Arithmetic. Another mystery as directed by Guru Matsyendranath Guru Gorakshnath worked on Abakalon and Samakalon which are nowadays Calculas. In Panchanan Mangal there are 5000 Pada or verses where every line is depicted the Algebra equation and the formula or Sutra.
Pingala and the Binary System:
Amidst this intellectual ferment, the mathematician Pingala emerges as a pivotal figure in the quest for zero. Little is known about Pingala himself, except for his work "Chandahśāstra," a treatise on prosody believed to have been composed around the 3rd century BCE. Though it was much before that. In ancient India before Sanskrit there were 4 language systems. Devas, Chandas, Bramhan and Lokayat. After Sanskar or compilation of these 4 language in became Sanskrit. In Chandas there are Hras or Laghu Swar and Deerhga or Long Swar. Here we found the Binary Pattern Where Deergha Swar is Guru Swar is 0, and Laghu Swar is 1. In this seminal work, Pingala introduces the binary system—a system of representing numbers using only two symbols typically denoted as 1 and 0.
Let me tell you a story about the binary system knowledge in India. Chess was invented in India. Once upon a time in Bengal, it was named Chausar. I will tell you why the name is Chausar in some other day. Indian mathematical system is not just mentioned mathematically. It was mentioned in different ways. Like a simple story, or some coded word where people feel it was a love story or a war story. Sometimes it is a fighting story between Deva and Asura. In ancient Bengal, that time its name was not Bengal it was Bongo (বঙ্গ) more than 6500years ago there was a regular culture of mathematics. In Panchanan Mongal, Chandi Mongal, and Annada Mongal. Three Mathematical systems are described in a poetic form. Panchanan Mongal is basically on Beej Ganit. Seeds of Mathematics. Nowadays people call it Algebra. Chandi Mongal is for Geometry and Annada Mongal is based on Arithmetic. Another mystery as directed by Guru Matsyendranath Guru Gorakshnath worked on Abakalon and Samakalon which are nowadays Calculas. In Panchanan Mangal there are 5000 Pada or verses where every line is depicted the Algebra equation and the formula or Sutra.
Now let me come to the story. In ancient India, there existed a legend of a King who found himself engaged in a fateful game of chess with a revered Sage. As the pieces moved across the checkered board, the King, ever curious, inquired, "Pray tell, what shall be the reward if you emerge victorious?"
The Sage, with a serene countenance, offered a simple request: grains of rice, doubling with each successive square of the chessboard. One grain for the first square, two for the second, four for the third, and so forth. The King, taken aback by the apparent modesty of the request, readily agreed.
As the game unfolded, the Sage's strategic prowess proved insurmountable, and victory gracefully embraced him. Now, the King, bound by his word, pondered the magnitude of the Sage's reward. How many grains of rice would fulfill the Sage's humble stipulation?
In ancient India before Sanskrit there were 4 language systems. Devas, Chandas, Bramhan and Lokayat. After Sanskar or compilation of these 4 language in became Sanskrit. In Chandas there are Hras or Laghu Swar and Deerhga or Long Swar.
The answer unfolded with staggering clarity: 18,446,744,073,709,551,615 grains—a monumental bounty, surpassing the rice production of the King's realm and the world combined for the ensuing two millennia!
This seemingly innocuous challenge, couched in the simplicity of grains of rice, concealed a profound mathematical truth—a truth that transcends the boundaries of time and space. In this allegorical exchange, the exponential growth of numbers reveals itself, illustrating the inexorable power of geometric progression.
Through this timeless tale, we glimpse the wisdom woven into the fabric of Indian folklore—a wisdom that transcends the ephemeral and imparts enduring lessons.
Within the contours of this legendary narrative, the Sage unveils his divine identity as Lord Krishna, imparting a profound lesson to the King. He graciously alleviates the King's immediate burden by offering a concession: the debt may be repaid gradually, over time, through a humble act of service—providing rice to pilgrims each day until the obligation is fulfilled.
In this convergence of myth and mathematics, the story unfurls the enchantment of numbers—specifically, the marvel of binary exponential expansion. Through each doubling of rice grains, the exponential growth unfolds, revealing the boundless potential inherent in numerical progression. Yet, interwoven with this mathematical revelation lies a timeless lesson in humility—a reminder of the virtue of modesty and service, embodied in the King's commitment to discharge his debt through daily acts of benevolence.
However, the tale's denouement is not confined to this benevolent resolution. It extends further, delving into the serendipitous discovery of binary numbers—a testament to the unpredictable nature of innovation and revelation.
In this ancient chronicle, buried beneath layers of symbolism and allegory, lies a profound truth—an acknowledgment of the symbiotic relationship between chance and discovery. Just as the Sage's challenge unfolded through the unforeseen ramifications of binary exponential expansion, so too did the discovery of binary numbers emerge from the serendipitous confluence of circumstance and inquiry.
Thus, the legend serves not only as a testament to the magic of numbers but also as a testament to the capricious nature of discovery—a reminder that sometimes, the most profound insights arise from the unlikeliest of sources, echoing the sentiment that truth often reveals itself in the guise of mystery.
While Pingalacharya's or Pingala's primary focus was on poetic meter, his use of binary sequences for enumerating syllabic patterns laid the conceptual groundwork for zero. By recognizing the significance of absence or nothingness in his binary notation, Pingala implicitly acknowledges the existence of zero as a placeholder—a precursor to its formalization in the decimal number system.
The Development of the Decimal Number System: The culmination of India's mathematical achievements is perhaps best exemplified by the decimal number system, also known as the Hindu-Arabic numeral system. Developed over several centuries, this system represents a monumental leap forward in mathematical notation and computation. At its core lies the concept of zero as a placeholder, enabling the representation of numbers of arbitrary magnitude and facilitating complex calculations.
The first explicit use of zero as a numerical digit is found in the Bakhshali manuscript, a mathematical treatise dating back to the 3rd to 4th century CE. In this ancient document, zero is depicted as a small dot—a symbol of profound significance that would revolutionize mathematical thought and reshape the course of human history.
Zero in Context: Philosophical and Cultural Implications:
Beyond its mathematical significance, zero holds profound philosophical and cultural implications in Indian thought. In ancient Indian cosmology, zero symbolizes the void or the primordial state from which creation arises—a concept echoed in the philosophical notion of Brahman, the ultimate reality. This metaphysical interpretation of zero underscores its deep-seated roots in Indian cosmology and worldview.
Moreover, the discovery and development of zero reflect broader trends in Indian intellectual history, characterized by a spirit of inquiry, innovation, and synthesis. The cross-fertilization of ideas between mathematics, astronomy, philosophy, and other disciplines gave rise to a vibrant intellectual tradition that continues to inspire and captivate scholars to this day.
In tracing the origins of zero in ancient India, we are confronted with a tapestry of intellectual achievement and cultural ingenuity. From the poetic musings of the Vedas to the mathematical treatises of Pingala and beyond, India's mathematical heritage serves as a testament to the human capacity for abstraction, innovation, and discovery. As we reflect on the profound significance of zero in shaping the course of human civilization, we are reminded of the enduring legacy of ancient India's mathematical genius—a legacy that continues to enrich and inspire generations of mathematicians, scientists, and scholars around the world.
What I told you about Acharya Pingala has already been proven by reputed scholars. But ancient Bengal and Nath Yogis and Siddhas from ancient Bengal still missing because of the negligence of the authorities and scholars and researchers. But from 1980 onward Avdhut, his Guru Avdhoot Atmananda, and Shree Siddhashram are tirelessly working on it.
