It was a crowd a rock band would have been envious of. The cavernous SAC (Student Amenities Centre) of IIT Madras was packed with enthusiastic under-grads, senior students from the two schools on campus, faculty and guests. The speaker, Manjul Bhargava, Fradd Professor at Princeton University, US, and winner of the Fields Medal in 2014, was talking on the eclectic combination of “Poetry, Drumming and Mathematics”.
The Professor spoke of his goal of trying to get young people to enjoy learning maths. This is very possible, he said, if we turn the teaching method on its head, and convey basic mathematical concepts through poetry and music, rather than through dry scientific concepts and examples.
The connection between poetry and mathematics goes back many centuries, said Bhargava, whose grandfather, a Sanskrit scholar, taught him the meter and rhythm of Sanskrit poetry and explained the phonetic logic in the arranging of groups of alphabets, based on where each set of sounds emanated from, already forging a link with a mathematical order.
Explaining how rhythmic combinations of short and long (laghu and guru) syllables form the basis of any great writing in Sanskrit and the Sanskritised languages, Bhargava demonstrated the various combinations that could be used to fill a poetic phrase of eight beats, which, he said, is the same as asking mathematically how many ways one can write ‘eight’ (as eight ones, or four twos, say) or how many ways one can write the number ‘n’ as a sum of ones and twos.
The ancients, he said, came up with an ingenious way of writing these numbers to obtain a general answer, with 7th Century poet Pingala proposing a sequence theory and Hemachandra (1050 AD) proving its effectiveness. What they prop osed was simple. To arrive at the number of possible combinations of 8 beats, write down the numbers 1 and 2, with each of the subsequent six numbers being the sum of the previous two. The result is the well-known numeric set: 1, 2, 3, 5, 8, 13, 21, 34. Yes, it’s what the world knows as the Fibonacci Sequence, though it was actually propounded a hundred years before the Italian mathematician was born! These Hemachandra numbers thus determined that there were 34 rhythm sets that could have ‘n’ number of beats (eight beats).
Metaphors make it easy
Our science and maths textbooks are so heavily influenced by Western thinkers that, unfortunately, this sequence is taught using the example of rapidly multiplying rabbits (for the Fibonacci numbers) instead of the far more elegant way they could be conveyed using poetic meter or even percussion beats.
To a roar of applause, Bhargava then proceeded to cement his show headliner status by moving the mathematical metaphor to percussion, demonstrating on the tabla how, again, the drummer can choose from 34 different arrangements of an eight-beat rhythm. Another 13th Century poet Narayana, also wrote a theory for any general set of rhythmic phrases.
The great poet-linguist Pingala had also come up with a vertical representation of numbers called the Meruprastara, which he called ‘the mountain of jewels’. These are essentially binomial coefficients that have extremely important implications in modern mathematics, in such areas as number theory, combinatorics, and so on. Sadly, we know this as Pascal’s Triangle, after the French Mathematician Pascal, who discovered them 2,000 years later!
Bhargava went on to show the lasting value of certain poetic devices used by the ancients to ensure that the understanding of several rhythm variations was preserved over the centuries. The poems they wrote to convey this knowledge were named after the gait of a tiger or a cobra, for instance, and were written in the same rhythm they were describing. Some of these rhythm sequences have present-day applications in searching algorithms involving data wheels (in sensors and dials, for example). They are used in many NASA missions to ascertain the specific orientation of a satellite. And they’re also used in card tricks!
Ending on a dramatic note, Prof Bhargava demonstrated a card trick to prove this point, guessing correctly the five cards picked at random by volunteers from the audience. Tantalisingly, he didn’t explain how he did it!