The objective of the movement is to ensure that our collective history of achievements does not stay forgotten in the folds of neglected manuscripts
The great physicist, Albert Einstein, once said, “We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made.” While many of us may know about zero and its origins in India, it remains a rueful fact that India’s contributions to global knowledge creation remains unattributed and uncelebrated.
Our history as an independent modern nation is 75 years young but our civilization is more than 5,000+ years old. Needless to say, the contribution of India to human knowledge is plenty, and what better a time, than the occasion of Azadi Ka Amrit Mahotsav, commemorating seventy-five years of independence, to initiate a concentrated and focused effort in this direction.
‘Dh?r?: An Ode to Indian Knowledge Systems’ is the Ministry of Culture’s flagship initiative in this direction. It is conceptualized as a series of lectures and discussions dedicated to specific areas of inquiry highlighting India’s civilizational achievements. Dh?r? embodies that idea of ‘continuous flow’ of knowledge and wisdom from one age to another, being adopted, questioned and modified over time so that we not only move ahead to the next level of insights across various fields but do so on the back of the work that is already available to us from our past.
It is my observation that outings and endeavors with connection to ancient past related topics often find polarizing responses due to lack of credible and rigorous evidence. Our attempt at program curation is mindful of the same and systemic efforts are being made to bring in academic scholars of the highest calibre to add the layer of rigorous reasoning and scientific credibility to these discussions.
Our first event under the aegis of Dh?r? was held recently and it was dedicated to “India’s Contribution to Mathematics Through Ages”. This unique conference saw lectures from Field’s medal winner Prof. Manjul Bhargava as the keynote speaker and other renowned scholars Prof. K Ramasubramanian, Prof. Parthasarathi Mukhopadhyay, Prof. Amartya Dutta, Prof. M. D. Srinivas, Prof. M. S. Sriram and Prof. SG Dani, as also international scholars Prof. Jean Michel Delire, Prof. Avinash Sathaye, and Prof. Clemency Montelle. The wisdom of India in mathematics captured during this conference was an eye-opener and a tribute to our system which promoted open inquiry, imagination, and synthesis. In what follows, we highlight some of the important topics that were discussed by scholars during the conference.
Binary Numbers: The Pingala’s Chandas-sastra is the first known description of a binary numeral system that dates back to 300 BCE. Listing of all the possible sequential arrangement of laghu (light or short) and guru (heavy or long) syllables — technically referred to by the term prastara — described by Pingala can be thought of as a binary sequence of 1s and 0s. Certain other techniques (nashta and uddisht) described by Pingala along with prastara form an important part of the study of modern-day combinatorics - in the name of ranking and unranking!
Indian Number System: The Bakshaali Manuscript is the first surviving reference of the Indian Number System. The algebraic properties of the number zero were first formalized in Brahmagupta’s Brahmasphutasiddhanta in 628 CE. The Hindu Number System was transmitted to the Arab world by around 800 CE and was popularized by the great Persian mathematician Al-Khwarizmi and by the great philosopher Al-Kindi. From the Arab world, it was transmitted to Europe by around 1100 CE. The Europeans thus mistakenly called it the ‘Arabic Number System’. To this date, most of us read this as the ‘Arabic Number System’ in our textbooks.
Negative Numbers in Mathematics: In the 7th century, among many other remarkable discoveries in mathematics, Brahmagupta also conceived of negative numbers and wrote down rules for working with them. He referred to positive numbers as fortunes (dhana) and negative numbers as debts (rina). His rule states: “A fortune subtracted from zero is a debt,” and “a debt subtracted from zero is a fortune”. Brahmagupta also knew that “The product of a debt and a fortune is a debt” which correlates to the idea that a positive number multiplied by a negative is a negative.
Binomial Coefficients: It is a well-known that Sanskrit verses are classified as syllabic metres (akshara-chandas) or moric metres (maatra-chandas) based on whether the rhythm gets generated by the repetitive pattern of a certain count of syllables employed or the number of beats employed in the metrical composition. The patterns are recognised, by assigning the value 1 to laghu syllable and 2 to a guru. The answer to the question- “How many metres can one construct for a given number of syllables”, is given by Pingala’s Meruprastara, which is an infinite mountain of numbers consisting of binomial coefficients. This Meruprastara also provides answer to the question ‘How many metres are there of n syllables having k laghus and (n - k) gurus?. Today, we study this Pingala Meruprastara by the name of Pascal’s Triangle named after the French mathematician Blaise Pascal (c. 1650).
Virahanka Numbers: The Indian prosodist, Virahanka (c. 700CE) came up with an ingenious answer to this question - Rs Rs How many kinds of patterns can be generated with a given number of beats? He asserted that we should write down the numbers 1 and 2. And then each subsequent number is obtained by adding up the two previous numbers. The nth number in the sequence 1, 2, 3, 5, 8, 13, 21, 34, 55, .... gives the number of different patterns that can be generated with n beats. One may recall that today, we know these numbers as Fibonacci Numbers after Italian mathematician Leonardo Bonacci, also known as Fibonacci. Unfortunately, Virahanka’s name is almost never associated with this important series of numbers used in multiple fields, including business, biology and computer science.
The Infinite Series for Pi: Madhava (c. 1400), the founder of Kerala School of mathematics and astronomy, for the first time in the history of mathematics discovered an infinite series for ? - one of the most mysterious numbers. This series which gives the exact value of ?, is generally referred to as ‘Gregory-Leibniz’ series in the textbooks of mathematics. Madhava also cleverly made use of this series-by inventing certain ingenious mathematical techniques — to obtain very good approximations of ? that was correct to almost 11 decimal places. This was indeed a landmark discovery which laid the foundations of the discovery of calculus in India.
Some of this may be news, while other bits may be partially known, but not celebrated. Our younger generation remains unaware and at times indifferent to this rich legacy. It isof course understood that topics like these require ongoing research, debate and cross pollination of ideas. Our efforts through the lens of ‘Dh?r?: An Ode to Indian Knowledge System’ is aimed at starting these conversations and debates and in ensuring that our collective history of achievements do not stay forgotten in the folds of some neglected manuscripts. We at the Ministry of Culture remain committed to spotlighting the myriad contributions of Indians across fields and to celebrate them as part of Azadi Ka Amrit Mahotsav and beyond. Come join us in celebrating India with pride.
(The writer is Secretary, Ministry of Culture, Government of India. The views expressed are personal.)