Sunday, February 15, 2015

Srinivasa Ramanujan: Jewel in Indra's Net

Why are we awed when we learn of Srinivasa Ramanujan's amazing results? He was self-taught, and provided no 'proof' for those results that conformed to the Euclidean / axiomatic model driving the western system of Mathematical study. Yet, as it has turned out over the hundred years since Ramanujan's works, a very, very high percentage of his results have been proven right by the Western system of mathematics. Very few of his results were found to be wrong, and a vast majority of his results were completely new - there is no evidence so far that the world knew about those findings before Ramanujan presented them. How did he do it?

Ramanujan himself attributed this remarkable success to his personal/ family deity, Goddess Namagiri, a feminine manifestation of divinity (in the dharmic sense), who 'gave' him the answers. The world takes this important piece of information with a bit of amusement, awe, and instead chooses to attribute Srinvasa's success to that unexplainable human attribute that the west has coined as 'genius'. Many Indians take pride in Ramanujan's 'genius', and the historicity that Ramanujan was born in India: a glowing reminder of India's once brilliant past, now extinguished; India got lucky with history, and Ramanujan won a gene lottery.

However, this does not appear to be a satisfactory enough explanation. Whatever this 'genius' is, it appears to be based on solid and systematic methods, and a lot of hard work, deep insights, and intuition. The story is that in England, as the professors there tried to teach Ramanujan new and modern areas of Math that he was not exposed to before, he was busy writing down new results. The story of a differently wired brain pulling results out thin air falls short.

The question arises: if there is a systematic method at work, then Ramanujan's methods must be reproducible by a human with a non-zero probability. So what is that system? Is this unique, or if not, where have we seen this before? Importantly, can we recover this systematic method and put it to use for solving today's and future problems?

YES, it is likely that:
a) there is a systematic method at work,
b) we have seen it before, and
c) it is reproducible.

Where and when have we seen it before? 
Yoga. Ayurveda. Vedanta. Many results have been derived in these areas of human discovery, after having been empirically validated and reproduced to the satisfaction of the Indian systems of verification (Pramana) for centuries now. The west, in places like Harvard University, and other centers of research have the sophisticated instrumentation and research funding to essentially reconfirm to their satisfaction, these astonishing Indian discoveries, or quantify and measure qualitative Indian findings. These verification studies are not trivial. Praiseworthy, painstaking studies in the west in the areas of psychology, medicine,  mind-sciences, Quantum physics, Human intelligence, Linguistics, Environmental management, Engineering, Management, Computer Science, etc. have quantified, validated, and embraced, bit by bit, section by section, these Indian results. New and beneficial products and services have been derived directly and indirectly from these Indian discoveries. This comes across as a replay of events that Ramanujan triggered in the area of Ganitha!

Based on these observations, it is possible that what Ramanujan achieved is not some random event. It is likely that his methods represent an application of a 'traditional' Indian approach to knowledge discovery. Paninian Ganitha versus Euclidean mathematics, if you will. Leading Indian expert-commentators like M.D. Srinivas have found Ramanujan's work to be representative of an illustrious body of work done by a sequence of brilliant dharmic researchers from Panini to Aryabhata to Madhava of Kerala. His results are no more astonishing that the amazing discoveries via Yoga, Ayurveda, and other dharmic methods that continue to benefit the cosmos.

Such methods neither claim, nor require, some magical-myth/supernatural monotheist God/random-genius basis.  Ramanujan's attribution to the Devi is not an isolated instance. Panini mentioned that the Shiva Sutras were revealed to him through Shiva's Damru. This attribution to the dharmic divine appears to be neither coincidental nor some zealous 'rush of religious blood'.

Two points to summarize:
a) Indian researchers state that the dharmic (Indian) approach to Ganitha represents a valid way of uncovering previously unknown facts that is different from the western approach of starting from assumptions/axioms and moves to theorems to newer theorems.

b) Furthermore, a state of mind required to generate such extraordinary clarity and insight can be induced via adhyatmic (inner science) techniques. These dharmic techniques can be learned by 'normal' humans from Gurus, and is not the sole preserve of wizards or prophets past.

Therefore, it is possible that new Ramanujan-type results can be generated in the future, and not just in Ganitha, but in a variety of fields, by learning and employing authentic Indian methods, in tandem with western instrumentation and techniques for verification.

Some screenshots from the IIT-Bombay Ganitha lecture series available on You Tube.

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