What poetry has to do with math

We stand to gain much from developing an understanding of ancient India, its deep and diverse ideas.

Written by Rohan Murty | Published:August 31, 2015 12:06 am
poetry and maths, poetry maths connections, Sanskrit poetry, history of poetry, india news, sanskrit poetry and maths, latest news, opinions Illustration by C R Sasikumar

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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  1. H
    heraclitus kapila
    Jan 26, 2017 at 3:49 pm
    Rohan , you miss the markdian epistemology is linked to mathematics and logic.tihs aspect can never come out through Pollock whose Abrahamic/ Aristotelian bias of the ubiquity of binary logic and deprecation of the subject in epistomology i s ubiquitas in Pollock. Critical analysis of Pollock shows that he is clueless about any links as they do not exist in western pjilosophy. I ahave aPhd in philosophy from American University and will challenge Pollock any day, as he is not even a Marxist and falls short of Walter Benjamin whom he uses as a prop but with whom he cannot be compared. Rohan you needed due dilgence before this appointment , or were you in a hurry to be accepted by the white man
    Reply
    1. S
      sree
      Aug 31, 2015 at 11:11 am
      Kudos to Murthy for boldly bringing about what was dismissed as right wing Hindu Lunatic statement all along in the statement "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. " One family / One party ruled us for 60 years since independence, and they left an intellectual environment, where any opinion other than "Secular Left Liberal discourse " was simply not allowed to raise its voice.. Hence, they are responsible for we having lived in a LESS open, tolerant and diverse society , than what India was in its ancient past.
      Reply
      1. B
        Bala
        Aug 31, 2015 at 11:26 am
        Amazingly bold and forthright.A clic expose on the kind of falsehood being perpetrated in our schools and universities even after gaining independence the name of "modern education". Time to overhaul the curriculum in our educational system lock,stock and barrel.
        Reply
        1. C
          crazy
          Aug 31, 2015 at 10:48 am
          Interesting article from Rohan Murthy
          Reply
          1. D
            Deepak Nautiyal
            Sep 2, 2015 at 1:17 am
            Great project with good intentions ... but be aware of western academics who has systematically digested/stolen indic-ideas and created false-propaa against Indic thoughts to establish western-superiority.
            Reply
            1. D
              Deshpande
              Aug 31, 2015 at 1:27 pm
              A very interesting and informative article
              Reply
              1. G
                Girish Ramaiah
                Aug 31, 2015 at 10:19 pm
                Even geometry originated in India. Various shapes such as circle, square,rhombus, etc were drawn symmetrically while performing any religious puja. Trigonometric functions were also discovered in india. There are many more. How many school children have heard of Ramanujan? Or Manju Bansal? A very good and timely article by Ronan.
                Reply
                1. H
                  Harsh
                  Aug 31, 2015 at 5:37 pm
                  Mathematics is a science of umption but life cannot sustain on umption, somebody has to work on the field to feed the parasites. The hard work of some people in the field of science brought us today’s prosperity but pity is that we never say even thanks to them but enjoy all the benefits of their hard work. Our contribution to the world in the form of Buddhism, which has been accepted by most of the potion in the form of democracy, is remarkable. However, we do not take pride in it as Buddhism discourages social and economical discrimination. I hope someday we will recognize our real strength and work collectively to bring glory to ourselves and around us.
                  Reply
                  1. H
                    Harish
                    Aug 31, 2015 at 11:31 am
                    If one reads Kalidasa she/he will understand how far superior he was to authors world around and of all times. Similarly Indian kids should be taught six 3 darshanas and tarka sangraha from an early age.
                    Reply
                    1. P
                      Pradip Dubhashi
                      Aug 31, 2015 at 8:56 am
                      Murty talks of idea of Indian education whose time has come. It would be worth Smriti Irani's while to take this further while formulating guidelines for restructuring the curriculam. She of course runs the risk of being accused of running the sffron agenda by the ingnoramusses amongst the political cl and the news media. I commend Murty for his an excellent espousal of structural reforms to bring benefits of civlisational inventory of knowledge to our young.
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                      1. B
                        BharatK
                        Sep 1, 2015 at 2:47 am
                        The world is a giant poetry. The feeling and expressions of all poems cannot be quantified. But poems can be composed to express mathematics, the language of the sciences.
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                        1. K
                          Karan Gupta
                          Sep 2, 2015 at 7:38 am
                          Only if Rohan Murty had set up world cl insution for studying India's clical heritage in India instead of Harvard, his search for the roots would have been much more appreciated. With funding Western Insution he left India's history in the hands of subverted minds with vested interests of promoting western imperialism.
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                          1. K
                            kulaputra kulaputra
                            Aug 31, 2015 at 12:31 pm
                            I was educated in Sanskrit clics. History was mostly European and American history. Indian history taught to us was full of distortions and perhaps romanticism overtook facts. I am still pondering how our great mathematicians actually proved any theorem or lemma or whatever you want to call it. No one till now seems to have described this with any conviction. Poetry is great but falls short of rigorous scientific proof for mediocre people like me who use mathematics and in particular principles of physics to design buildings and bridges. Thus, we should stop romanticising and create scientific papers on actual proof (pramana) methods.
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                            1. M
                              malavika
                              Sep 2, 2015 at 8:31 am
                              Murthy Clical library is the problem. Giving control of our scriptures to Goras is a sign of mental Slavery. It is ll the more sinister since Sheldon Pollack thinks Sanskrit is a dead language. The word he uses is clical ( google clical language). So he thinks he has the authority to interpret it for US. The the ultimate Colonization. I wish this rich kid Rohan spend his money on himself rather than supporting Hinduphobes.
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                              1. M
                                malavika
                                Sep 2, 2015 at 8:31 am
                                Murthy Clical library is the problem. Giving control of our scriptures to Goras is a sign of mental Slavery. It is ll the more sinister since Sheldon Pollack thinks Sanskrit is a dead language. The word he uses is clical ( google clical language). So he thinks he has the authority to interpret it for US. The the ultimate Colonization. I wish this rich kid Rohan spend his money on himself rather than supporting Hinduphobes.
                                Reply
                                1. M
                                  malavika
                                  Sep 2, 2015 at 8:31 am
                                  Murthy Clical library is the problem. Giving control of our scriptures to Goras is a sign of mental Slavery. It is ll the more sinister since Sheldon Pollack thinks Sanskrit is a dead language. The word he uses is clical ( google clical language). So he thinks he has the authority to interpret it for US. The the ultimate Colonization. I wish this rich kid Rohan spend his money on himself rather than supporting Hinduphobes.
                                  Reply
                                  1. M
                                    malavika
                                    Sep 2, 2015 at 8:31 am
                                    Murthy Clical library is the problem. Giving control of our scriptures to Goras is a sign of mental Slavery. It is ll the more sinister since Sheldon Pollack thinks Sanskrit is a dead language. The word he uses is clical ( google clical language). So he thinks he has the authority to interpret it for US. The the ultimate Colonization. I wish this rich kid Rohan spend his money on himself rather than supporting Hinduphobes.
                                    Reply
                                    1. N
                                      Narayana
                                      Aug 31, 2015 at 11:11 am
                                      Very well balanced article. Points are nicely developed. Informative plus interesting.
                                      Reply
                                      1. S
                                        suman
                                        Aug 31, 2015 at 4:03 pm
                                        While it is true that there is a lot of enriching stuff for us to enjoy and indulge in, which comes from our own land, I dont see why it needs to be connected to maths, in order to be worthy of attention. I, along with a sibling have seen the fun of trying to read through Kalidasa (try the prakrit spoken by the female characters, and it to marathi/bengali of today, it is sheer fun), and the Natya Shastra. We could promote the perusal of Kalidasa and other such secular/literary/aesthetics works as fun activities and bring them to life. Clical music is another such candy that can be handed around freely. But, do we/you really want to share it freely, without jealousy, believing that more we share, the more these things grow? Do we want to separate the sensible appreciation and practice of these arts from empty, fanatic flaunting? There lies the rub.
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                                        1. R
                                          RJ
                                          Aug 31, 2015 at 9:04 am
                                          My friend, I am in my 40s; I too pondered over the questions/issues you raise in your wonderful article; I believe I have found the reason behind the "structural" reasons behind the state of utter ignorance among our citizens about our civilizational contributions. It is because of a deliberate plan executed by the leftists of the congress-communist parties to erase all traces of national ideny based on anything from the pre-moghul era. These leftist plotters did their best to manufacture a false national ideny based on the moghul dynasty - with active support from the congress party because it suited their political designs. Since the congress party ruled the country for several decades, this leftist design permeated every aspect of India, from school books to University education to historical research to news media. By and large, the leftists succeeded in their plan; over 60 years, we have become a nation of zombies with no connection to our civilizational heritage, and continue to receive a sterilized education. But I have hope. The Indian youth is beginning to realize that the leftists have pla a mive fraud of monumental magnitude on them. I think that the near total rejection of the congress party last year is a sign of revival among the youth. I am optimistic about the future.
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                                          1. R
                                            Ramesh Grover
                                            Aug 31, 2015 at 7:56 am
                                            A revealing article rooted in depth of human mind, and I who have grown long years ago share and see it in the same light. Factually, we are the world and the world is us in every possible way. As such, past is not ignorable, as we are its outcome and have to face presently realities with a very old mind. Renewal or generation of a new mind emerges only where the old is fully understood. Thus to ignore the intellectual dynamism of ancient indian mind is an invitation to live in a partial world of reality. One must understand our own mind scape as much as we do to another part of it drawn from the west.
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