Over the past year, I have heard my friend, mathematician Manjul Bhargava, give several public lectures on the deep connections between poetry, Sanskrit and mathematics. Like many other mathematicians before him who have written or spoken on this topic, Manjul gave an array of examples that demonstrate the tremendous depth and contributions made by ancient Indian (for the purposes of exposition, stretching perhaps from present day Afghanistan to Burma) philosophers and poets to mathematics, often before their counterparts in Western societies did the same. Manjul’s quintessential example is from roughly 11th century India, when Gopala and Hemachandra discovered a delightful connection between the number of syllables in Sanskrit poetry and mathematics. The answer, it turns out, is what we now call the Fibonacci series (also appears in the number of petals in certain flowers in nature), which was eventually rediscovered by Leonardo of Pisa, better known as Fibonacci, about 50-80 years later.
That there should be an inherent connection between the number of syllables in Sanskrit poetry, a product of human thought, and the number of petals in flowers in nature must startle any reasonable person. Another extraordinary example that Manjul highlights is the discovery of the binomial structure hidden in Sanskrit poetry, as discovered by the ancient Indian poet Pingala, roughly in 200 BC. This was about 1,800 years prior to the French mathematician Pascal’s Traité du triangle arithmétique, which we today learn as Pascal’s triangle. Other examples include the use of techniques that resemble modern error-correcting codes, synchronisation, and formal language definition in Sanskrit poetry and prose. These are all modern inventions (or reinventions, in some cases) that impact almost every aspect of our lives, from computer languages to wireless communications.
It would, of course, be foolhardy to claim the ancients invented or knew of computer languages or wireless communications. That would be like claiming Copernicus built space ships to fly to the moon. Rather, what these examples do highlight is that a long time ago, in or near the region we live in today, there existed a thriving civilisation that produced extraordinary intellectual thought and ideas which continue to have fundamental connections with the way we live today. We appear to have lost knowledge of this ancient past through the vicissitudes and vagaries of time. And with it, a significant source of pride and the ability to influence modern Indian identity. Few people of my generation appear to be aware of these facts.
Part of our ongoing ignorance of the past appears to be structural. Case in point: At my high school in Bangalore, as part of the ICSE syllabus, we read Hamlet, Merchant of Venice, works by Wordsworth, Tennyson, James Joyce, Dickens, etc. We even read Walt Whitman wax eloquent about the end of the American Civil War and Abe Lincoln’s death in “O Captain! my Captain! our fearful trip is done”. Never mind the fact that none of us in class knew what a civil war was at the time, or that America had one, or how or why Lincoln died. We read the tremendously uplifting lines from Tennyson’s “Ulysses”: “To strive, to seek, to find, and not to yield”, all while lacking the context of ancient Greece or even knowing how to say “Ithaca” (we learnt it as EYE-THA-KA). We had little or no context for these strange ideas, words, phrases, stories, heroes and worlds.
And yet, we read these poems, short stories, novels, and wrote essays about them to pass our school exams. This was an enjoyable experience and I would do it again. However, such an educational experience and exposure was severely stunted in its diversity of thought and ideas. What strikes me as odd is that we students never read any classics that originated in this part of the world — that is, ancient India — despite having a cultural advantage of perhaps being able to understand the context better. We knew of no texts, poems, plays, great prose, science, mathematics, civics, political life or philosophy from 2,000-plus years ago from ancient India. My friends and I, stereotypes of the urban educated populace, remained entirely unaware of the intellectual contributions of this past. The most we seemed to know were a couple of random dates and trinkets of information on the Indus Valley civilisation, Ashoka and Chandragupta Maurya, all of which seemed almost perfunctory and without any depth in the manner we read them in school.
As students, we were well versed with Plato, Aristotle, Pythagoras, Copernicus, Newton, Leibniz, Pascal, Galois, Euler, etc, and their tremendous contributions to mankind. And yet, most of us had never read about Aryabhatta, Brahmagupta, Pingala, Kalidasa, Hemachandra, Madhava, the Nyaya or Mimimsa Sutras, or the Therigatha.
But why bother with any of this? After all, we were never part of these accomplishments and they were so long ago, by a people so far removed from today’s reality, that attempting to create any link to the past is surely irrelevant. But I would argue this discovery of the past is no less relevant than what we already study and acknowledge in the earlier cited examples in our schools and colleges. Besides, these sources of knowledge from ancient India are products of creative human thought and hold genuine value for the world, irrespective of where they come from, or geographic affinities. For example, any child on this planet will find mathematics far more amenable when learning parts of it through poetry, as opposed to the dry, dull methods espoused by most mathematics pedagogy today.
While national identity is a complex phenomenon, perhaps in some proportion it relates to the intellectual contributions made by societies to help advance knowledge and improve the human condition. Newton is a hero to many like me, who read in wonder about how he unravelled the basic laws of the universe. Great literature and philosophy from Western societies have helped us reflect on the human condition. Such examples from the Western world have magnified our respect for societies that could harbour, enable and encourage such curiosity. In the same vein, we stand to gain much from developing an understanding of ancient India, its deep and diverse ideas, which are no less extraordinary than those we have come to marvel in Western civilisations. I am not suggesting we lose respect for contributions made by other societies or civilisations, or that everything of note was discovered in this part of the world. Rather, we ourselves have much to gain when we dispassionately discover, examine and acknowledge the intellectual history of ancient India. We may be surprised to find it was perhaps a more open, tolerant and diverse society than even the one we have lived in since Independence. If you need more convincing or inspiration, look up Manjul’s talk on YouTube. Or try reading the Therigatha.
The writer, junior fellow in the Society of Fellows at Harvard University, is founder, Murty Classical Library of India.
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