Saturday, January 7, 2012

Art of complexity

In the Journal of Indian Mathematical Society, Srinivasa Ramanujan posed a few very interesting puzzles. One of the first problems he posed and a very intriguing one belongs to  recursive category.

Upon persuasion, Ramanujan himself gave the answer: 3

Most beginner students are put off by the complexity of Sanskritam language. The way Sanskrit is taught in schools and the text books that start off with all conjugation combinatorics are mostly to blame. Complexity probably does not daunt them when the students opt for French, German or Spanish as their "second" language. When studying these languages, the students start out with a tabula-rasa, if I may borrow from Immanuel Kant. They are not exposed to the literature there of right away. But in Sanskritam, in our everyday life we are already exposed to several subhashitam-s, sloka-s and stotram-s. There are literally tens of thousands them, not to mention the maha kavyas and other works. Obviously one cannot know them all. But the sheer volume can intimidate the students right away. Apart from that, there are the pre-concieved notions and biases about Samskritam. Every Indian state, region and individual have an opinion on Samskritam.

During the Austin Yamunotrii 2011 Samskritam Family camp , Smt Sharada Varadarajan mahodayaa gave an interesting speech about how a same idea can be represented in simple or complex language.

"Boy eats food"

can be translated as "baala: annam khaadati", which is simple enough to understand. (a-karanta: + a pan-Indian shabda 'annam' + a parasmaipada verb)

Or it can be translated as "shishu: odanam ashnute" (u-kaaranta + rice-food + a non-inituitive aatmanepada verb).

Coming to think of expressing ideas in complex terms, why was complexity deliberatey favored by Sanskritam poets? The Darwinian evolution of intellect does not seem to apply to the Indian experience. In the Indian lore, the ancients were always considered people of vastly superior intellect. I am not talking about the divine beings, but the maharshis, muni-s, siddha-s, poets - ordinary people who elevated themselves to a much higher level of consciousness. If evolution means man becomes more intellectual, how could the ancient Indians think in complex terms, thousands of years earlier? What was the need for creating complex tongue-twisting shlokas, stotram-s, stuti-s or those that would read meaningfully back-to-front, while a simple "namami", "vande", "nama:" would suffice? Does the "phala" of shloka depend on the complexity of the recited ?

The reason is the same as George Mallory gives on why would somebody go through a difficulty of climbing a mountain: "Because its there."

Why would the ancient poets conjure up some of the most complex and intricate shlokas, chandas and poetry? Just because Sanskritam allowed them to.

The structure of the language let them run amok, at times wildly, in the forest of intellectualness. The fluidity of the language let them soar their imaginations in all directions without compromising the school-teacher like strictness of the grammar. The richness of the language yielded the fruit of satisfaction, that in turn enriched the language like a feedback amplifier.

Complexity can also be humorous: Harshavardhana's Naishadiyacaritam is supposed to be so complex, that Harsha himself rewrote it a few times to make it simpler.

A poet asks Harsha: kim cikIrShasi ? [What do you want to eat?]
Harsha: shemuShImuShimAShamUShe [I want to eat urad dal to become dull]

Harsha's mind was probably genetically wired to think in complex terms. He wanted to eat urad dal to make him dull, to think in simpler terms. But he could not express his wish in a simple way! Urad dal is supposed to make one dull of intellect. Harsha wanted that to make him dull to think in simpler terms!

Like it or not, the Ramanujan's formula is beautiful and the recursiveness mesmerizing. We may dislike complexity, run away from it or curse it, but it is out there. If we learn to appreciate complexity, it may not daunt us no more.
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