Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts

Wednesday, May 27, 2009

Genius and Intuition

Following is an article I had written for Petals, a portal for self expression at my first job

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Intuition though quite an inexplicable phenomenon yet attracts attention from scientists, mystics and laymen alike. I will take intuitions in the context of geniuses with specific reference to Ramanujam as portrayed in a biography aptly named "The Man who knew Infinity".

The book attempts to take a holistic view of Ramanujam's life, his early years, dominant yet caring mother, his leaning, place in which he lived, the soil on which he walked on. It attempts to describe an oriental mystic and genius meeting the renowned eccentric mathematician Thomas Hardy. This is a recurring theme and comes up in subtle ways, clearly chalking out a line between east and west.

Second aspect of the book is the chasm in which the book is written. This chasm is the view of phenomenon of intuition as seen by the Orient and the Occident. The divide overshadows any other perspective of events described in the book.

Where did Ramanujam's magical intuition come from? Was his work a fluke (though a string of flukes, if this is true)? Was it because of his religious beliefs as he used to claim? We are not answering these questions, for the questions and asking of these questions is what matters to us here.

In his prolific book "The Argumentative Indian" written by Nobel laureate Prof. Amartya Sen also discusses this aspect in a different manner and slightly different context. Prof. Sen takes example of Indian mathematician namely Aryabhatta and Varahmihira. Their work and source of inspirations in some or the other ways were always likened with their religious beliefs. The point is not whether their religion beliefs made an impact or not. The point which he puts forth is why this question is asked only in cases of oriental thinkers.

In Ramanujam's case, the interest in mystic gets accentuated because he himself told appearances of goddess Namagiri, who informs him all the solutions which became humongous feats in mathematical intellect. He had a deep interest in astrology – not as an amateur, nor a practitioner, but as a serious pursuit which is evident in the prediction of his early death made by himself.

Ramanujam was a strange dichotomous character for the west. A religious, mystic genius in mathematics who worked on intuition rather than rationale, his works were flights of fancy. Flashes of intuitions, boisterous mathematical claims without a proof at hand were commonplace with him. Though many of his claims finally proved to be wrong, the ones that were right, proved to be prolific.

His life also gave a picture of colonized India, where a genius of his stature had no formal education to make him eligible for research work. His brilliance was scoffed off in his own land and would be recognized truly, albeit with apprehension in west.

Thursday, December 20, 2007

गुगली गणित की

a: Research has shown that drinking beer can be good for health by improving digestion, hydrations and couple of other 'tions'. [Accompanied with link to a really low quality, run of the mill article by a popular web portal]

b: Yeah right! It suggests test was done on 25 students they didn't even bother to go beyond their department I guess. Aam ke aam aur guthliyon ke daam! Aye boyz lets haav sum beaah and run for the gawd damn sayks, gotta shauw sum vital staatistix. I would say the perfect work life balance

b: A cutting (no bleeding, slashing and decapitating) research has shown that birthdays are good for longevity! The more you have the longer you live

a: Yeah wacko, another research shows 2 comes after one in series of natural numbers.

This lead me to a diversion towards a geek book I had read titled 'Godel, Escher, Bach' by Douglas Hofstader. In it there is a part where he explains what those mathematicians lost in formal theory do when they are not performing compulsory chores of life.

Some guy named Peano (not it is not a misspelled Piano) did some break through work in this field. These blokes do some really ass kicking work using a snazzy sounding words like axiom, premise, intrinsic property. To deconstruct the crap this guy laid the foundation by propounding few axioms like:

0 is a natural number.
For every natural number n, S(n) is a natural number.
S is successor function so S(0) = 1 and 2 = S(S(0))

Now this might sound like a hyped Hindi Cinema flick gone dud like 'Roop ki Rani Choron ka Raja', 'Asoka' or recent 'Aja Nachle'. Talking of fundu mathematics and then saying 2 follows 1. Even my housemaid with limited knowledge of mathematics knows 2 comes after 1. And what is this business about S? Filling up your pages of thesis by larger font, line height and paragraph setting is different but ssseriously duude flooding it up with S is a lot to grasp. Sounds more like a precursor to Kta Kapoor or kRkakkekskhk kRkokskhkaknk.

Well it seems Peano's work was used by Godel to derail Hilbert's Program. The guy like a Bond movie's megalomaniacs wanted the mathematical world to be conquered [Not Safe for Work because you might go mad till you hit the full stop or bang your boss's head]. Like Sauron in Lotar (LoTR) wanted one ring to rule 'em all. Hilbert's grand scheme was to give some mathematical system which can prove all other mathematical systems (like boolean arithmetic, vector algebra etc etc all those things you hated in school/college). So our Bond like Mr. Godel gave Hilbert's medicine back to him by proving his shit can't prove his own shit (:-0, don't ask me further about this else i shall puke a lot of S's and greek symbols on you). Mathematicians cohabit their own little crazy world throwing conjectures, hypothesis, axioms and what not.

SSSSSSSSSSSSSSSSSSShhhhhh.... koi hai!