Origins and interconnections
The Big Picture
The Birth of Chess – The Silk Road – The Luminaries of Gupta Mathematics – Vedic Architecture and the Chess Board
Our story begins roughly 1,500 years ago along the Silk Road in a kingdom of the Gupta Empire. The time of the Gupta Empire is period known as the Golden Age of India. Philosophy, art and science flourished. Kalidasa composed epic poems of devotion, buddhism grew alongside a renaissance of the hindu pantheon, there was political stability, economic abundance and intercultural exchange with the Chinese in the East and Romans in the West. This thriving environment brings us the legend of the birth of chess.
At the time and place of our story dice games were the most popular form of entertainment. The King himself was very fond of games, but he recognized a disturbing aspect underpinning the most popular game of the time, Nard ( a version of modern day backgammon). He worried that since Nard was a game whose outcome relied so heavily on the role of the dice, it left too much up to chance, to randomness, to luck. He believed that humanity’s greatest gifts was that of self-determination, and that the rampant play of Nard was eroding his subjects’ faith in their ability to take responsibility for the course of their lives.
So he ordered his counselors to publicize a contest throughout the entire kingdom; whoever invented a game whose outcome was based solely on the wisdom and skill of the better player, no luck involved, could have his choice of any prize in the kingdom. Months passed and the king despaired as no suitable game had been brought to him. One day the yogi Sessa appeared at court and finding the king in his state of anxiety asked him what the trouble was. The king explained his concerns, and to his great surprise Sessa merely laughed. Sessa told the king he would show him such a game, and would only require for payment enough grain as to fill the Astapada (the term used then for the 64 square board we now know as the chess board).
The king was in a state of shock, he had offered any reward in the kingdom and Sessa only asked for grain.
The Astapada is based of the Vastu Purusha Mandala
Sessa explained to the king that he would require one grain for the first square, two kernels for the second square, four for the third square, and so on and so forth doubling the amount for all sixty four squares. The king, bewildered, was tempted to dismiss Sessa from the court thinking he was a mad man to make such a request. But his curiosity had been aroused and so he agreed to Sessa’s price, asking him to explain the game. Sessa laid out the astapada and fashioned pieces representing the four divisions of the Indian Army– soldiers, elephants, horses, chariots, then the king and his minister. The name of the game, he explained, was Chaturanga (meaning four-armed, or four brothers in arms) and it is the precursor to the game we play today called Chess.
The number of kernels of grain owed to Sessa was enough to fill a silo with a height of twice the distance from the earth to the sun
The king was thrilled and he called on his treasurer to pay Sessa the reward; the treasurer however was having trouble figuring out the exact total of grain Sessa was owed. In those days there were no electronic calculators, or even abacuses, all calculation was done by hand, and while it was easy to figure out the number of grains for the first few squares the number was rapidly growing larger and larger. As the legend has it the king had to hire mathematicians from neighboring kingdoms and after long calculations they came to the number of kernels of grain owed to Sessa, 18,446,744,073,709,551,615, enough grain to fill a silo with a height of twice the distance from the earth to the sun!
Upon learning of this sum the king realized that chaturanga (chess) was much more than just a game, but a system for teaching mathematics, reasoning, and other disciplines of the mind. He beseeched Sessa to stay at court to teach him and his heirs the secrets of the game so that they may have the advantages elicited by its play for generations.
Silk Road
The Silk Road was not a singular road, but rather a sprawling network of interconnected trade routes that spanned from East Asia to the Mediterranean, connecting various civilizations. Its name originates from the trade in silk, but it was also used to transport a plethora of items: spices from Southeast Asia, precious metals from the West, and numerous other goods like ivory, gemstones, and ceramics. But more than just goods, the Silk Road facilitated the exchange of ideas. Religions like Buddhism spread, art forms intermingled, and scientific knowledge was shared.
Gupta Mathematics and the ‘invention’ of zero
The Gupta period’s advancements in mathematics included the concept of zero, decimal system, foundational algebraic principles, and early formulations of gravity.
Brahmagupta and Aryabhata are seminal figures in the annals of ancient Indian mathematics, each making groundbreaking contributions that would shape the trajectory of mathematical thought.
Aryabhata, in the late 5th century, composed the “Aryabhatiya”, a seminal treatise that consolidated various aspects of mathematics and astronomy. One of his notable achievements was the approximation of pi accurate up to five decimal places. In the realm of trigonometry, Aryabhata listed sine values at intervals of \( \frac{3.75}{90} \) degrees in a table, and he introduced the concepts of sine (jiva) and cosine (kojya). He also proposed that the Earth rotates on its axis, a revolutionary idea for his time.
Brahmagupta, working in the 7th century, authored the “Brahmasphutasiddhanta”, an extensive work on astronomy and mathematics. He is especially renowned for his work with zero. Not only did he recognize zero as a distinct numeral, but he also set forth rules for its mathematical operations, addressing its use in both multiplication and division. Furthermore, Brahmagupta delved into the properties of negative numbers and, in doing so, became one of the first to understand them as “debts” rather than just abstract concepts. In the domain of algebra, he made significant strides, solving various quadratic equations and laying down rules governing them.
Together, the profound contributions of Brahmagupta and Aryabhata provided foundational advancements in algebra, trigonometry, and arithmetic, their insights echoing through mathematical scholarship across geographies and eras.
The Vastu Purusha Mandala, a central concept in traditional Hindu architecture, symbolizes a cosmic diagram and a metaphysical plan. It maps out an intricate grid, subdivided into smaller squares called “padas,” each carrying a unique significance. At the heart of this Mandala lies the “Astapada,” an 8×8 grid, simultaneously serving as an architectural blueprint and as the board for strategic games like Chaturanga, an ancestor of chess.
This Mandala does more than just portray symbolic meaning; it offers precise guidelines for architectural design. Each pada within the Mandala is associated with a particular deity or attribute, and these associations play a pivotal role in deciding the spatial arrangement of structures, rooms, or even entire cities. For instance, while laying out a temple, the padas guide where specific deities should be placed, ensuring that each part of the structure resonates with the intended spiritual energy.
In essence, the Vastu Purusha Mandala and Astapada provide a profound blend of symbolism and practicality in Indian architectural practices, ensuring constructed spaces are in harmony with both their spiritual intent and functional requirements.
Vedic Architecture and the Birth of The Chess Board
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A Primer on Indian Philosophy
The Gupta Empire, flourishing between the 4th and 6th centuries CE, was not only a period of considerable political and artistic achievements but also a golden age for Indian philosophy. Several schools of thought, both orthodox (accepting the Vedas as authoritative) and heterodox, blossomed during this era.
Vedanta
Expanding upon the Upanishads, Vedanta delved deep into metaphysical questions about reality, consciousness, and the ultimate purpose of life. One of its key tenets is the idea of Brahman, the universal soul, and its relationship with Atman, the individual soul.
Buddhism
Although its origins predate the Gupta period, Buddhism underwent significant evolution during this era. Emphasizing the Four Noble Truths and the Eightfold Path, it offered a systematic approach to end suffering and attain enlightenment.
Nyaya
Known as the school of logic, Nyaya emphasized rigorous logical analysis to understand the nature of reality. It established frameworks for debate, logical reasoning, and epistemology, fostering intellectual discourse.
Vaisheshika
Propounded by Kanada, this school was materialistic, postulating that everything could be reduced to a finite number of atoms. It categorized the universe into six categories: substance, quality, activity, generality, particularity, and inherence.