Friends

A feast for friends in my car,
An intention to travel far,
We took our turns on the steer,
Mixed our joy, shared our fear.

Just when it started to look real sleek,
'A' said he wanted to pull over, take a leak,
I stepped out to check the vehicle's rear,
I saw 'A' steal away and disappear.

'C' cried, "What happened to A and his spine?"
We debated this question over a jar of wine,
'B' announces, "Charlatans we will be no more!"
Before he sells himself to a swinging whore.

'C', with his acumen, could join the links,
said he knew this friendship was a jinx,
said only passionate fools dream the sky,
As he gulped his wine and spat goodbye.

I sat a while, finishing my glass,
The kind alcohol flashed my past,
I pondered upon the auguries of my life,
probably destined for the butcher's knife.

Resuming my journey minus my crew,
I felt an urge to go through and through,
I pocketed myself an another mile,
As 'B' came back with his apocryphal smile.

Sheepishly sorry to not resisted her lip,
He lamented to have broken our fellowship,
Then promising never to leave my side,
He convinced me to resume 'our' ride.

We resolved to drive by a constant decree ,
While keeping an eye out for 'A' and 'C'.

Unknown

Here, on the level sand,
Between the sea and land,
What shall I build or write
Against the fall of night?

Tell me of runes to grave
That hold the bursting wave,
Or bastions to design,
For longer date than mine.

-Unknown Poet (Extracted from an unreferenced quotation)

Ramanujan (continued...)- Part 2.

So where were we earlier? A young boy of 17 infatuated with mathematics... unsatiated with what the school curriculum or available textbooks of that era provided.... with acumen and originality par excellence, was hungry for more. An answer came in the form of an old and outdated textbook titled, `Carr's Synopsis of Pure and Applied Mathematics'.

Actually it was hardly a textbook, not even close to being one. It was only because of Ramanujan that we know of this book today, else it was already out of print 50 years before Ramanujan's time.

Carr, an englishman and the author of the text, was not a professor in a university nor a very competent mathematician. He was, in fact, a private tutor of mathematics who coached students preparing for the Mathematical Tripos. The Tripos was a highly tough and competitive examination in mathematics which was taken by college students aged 20-21. Excelling in the Tripos was considered a great honour and the toppers in this examination were called 'Wranglers'. Being a Wrangler more or less guaranteed you a full scholarship to pursue Mathematics at Cambridge or Oxford or any college of your choice. The Tripos is one of the oldest examinations in the world, and though it has changed in format and structure, it still exists. Infact great english mathematicians like James Clerk Maxwell (who formulated the first comprehensive mathematical theory on electromagnetism and is famous for the 4 Maxwell's equations of electromagnetics) , G. H. Hardy (who shall feature in this monograph later), Lord Kelvin (famous physicist who worken on electricity and thermodynamics) and Geoffery Taylor (one of the greatest fluid mechanicians ever) were senior Wranglers in their time, just to name a few.

So coming back to Carr, who himself had passed the Tripos, though not as a Wrangler, was a popular tutor for the examination and ran classes around 1840-1860. It was for these classes that he had prepared the Synopsis which was more of a compilation of 5000 theorems in algebra, integral and differential calculus, the theory of equations, number theory, continued fractions and trigonometry. It was hardly a text book, in the sense that it contained very little theory. But what it did have was a step-by-step chronology of mathematical theorems each a little more challenging than the previous one. Since this was not a textbook, the author had not bothered to provide detailed proofs anywhere throughout the text. Most formulae and theorems were simply stated and for some difficult ones, a couple of lines attempting to delineate the rough solution strategy were provided. It was with this primitive text that Ramanujan began his adventure into advanced mathematics. It is probably one of the most intriguing facts that such a primitive book should trigger the genius of a man, as he began working through each problem in the book, each solution being a piece of original research for him. More importantly, as Ramanujan churned mathematics out of the book, the book inspired mathematics out of Ramanujan. He started filling up his `notebooks' (which would later become famous as his legacy and remain as poseidon's treasure for mathematicians of the 20th century) with original theorems of his own working with force and vigor. By the time he was 20, he had developed his own special methods of constructing magic squares, his own theory of modular equations and continued fractions and his own theory of divergent series (which though later found to have a lot of inconsistencies was nonetheless remarkable to have originated from an amateur mathematician). There is one last time I should like to mention about Carr and his book. Other than extracting the genius out of Ramanujan, the book had another singular effect upon his methodology of working out problems that has left its mark in his notebooks. Throughout his notebooks, Ramanujan does not care to write detailed proofs for any of the 3000 theorems that he conjured himself. He barely outlines the proof and it hardly makes any head or tail to the innocent reader. Ever since his death many mathematicians tried to work through his notebooks, most of them giving up because they found it eating up their time. It is just recently, after work for more than 20 years that Bruce C Berndt, a mathematics professor at UIUC released a 5 book series that provides a detailed exposition of Ramanujan's work as an amateur mathematician which is hidden in his notebooks. His work as a professional mathematician is yet to be mentioned.

(To be continued.....I try to be regular at this but I'm afraid of losing inspiration and leaving it half baked!)

Importune

Don't give me a second chance. Just kill me before I realise I've missed the first. I have got used to chicanery.

Awake!

We live, we die and death not ends it!

Diogenes and me (Ramanujan updated!)

Diogenes of Sinope was a famous Greek philosopher who belonged to the class commonly referred to as the 'Cynics'. He was a pupil to one of the descendants of Socrates and was introduced to the ascetic way of life by his master. Infact he was imposed to such a severely austere way of life during his initiation years by his master's will that it almost hung over the edge of brutality. It was probably these years of extreme disregard for all attachments, not only at the metaphysical level, but also at extreme physical levels that Diogenes evolved as a major amplification of his master's image, and became the epitome of cynicism and austerity in the Greek legends. All his life he lived in a tub, had raw onions for his meals and slept over a bed of bones.


In due time, Diogenes only intensified his practice austerity. He gave up his clothes and in no time was left with only a single possession- A cup for drinking water out of the fountain. It is said that he once observed a dog licking water from the same fountain in its usual way and that made him realise the futility of the cup that he kept. He threw his last possession away too. When asked how to avoid sexual temptation he began masturbating. Later on he remarked on hunger, "If only I could soothe my belly by rubbing it."

A couple more fables of Diogenes are famous, one that gives us a peep into his philosophy of cynicism. It is said that he used to roam around in broad daylight with a lighted torch in his hand and when asked what he was doing, he'd say, "I'm looking for a honest man!" It is said that, once Alexander, the great himself came to meet Diogenes, having heard about his legend and remarkability. Impressed by his outspokenness and wit, Alexander asked Diogenes to demand any boon he desired for; to which Diogenes requested the great emperor to stand out of the way of his sunlight!

Alexander is known to have remarked, "If I would not have been Alexander, I should have liked to be Diogenes!". Both Alexander and Diogenes incidentally died on the same day. Alexander was 33 and Diogenes was 90.

Diogenes was sometimes a man with singularly gross habits, and the word that comes to my mind when I picture the way he would have lived each of those disgustingly happy days spanning 90 years of his lifetime is- 'grotesque'. Infact, the citizens commonly referred to him as "The Dog". But I know for sure, that he would have spat on my face if he saw me make this miserable analysis of his life; like he did on the face of a 'charitable' man who invited him to his house for dinner among the aristocrats. But Diogenes was a happy man. And he probably found what he was looking for in those 90 long years living naked on a pile of bones and feeding on onions.

(monograph on Ramanujan shall be continued...bit by bit in dollops in the same place!)