A Mathematician’s Apology

Reading G.H.Hardy's 'A Mathematician's Apology', I couldn't help myself feel a little unworthy (will elucidate later). Hardy puts forth fitting arguments for mathematics and exalts the act of pursuing mathematics for the sake of mathematics and without being worried about its implications. The treatise was written when he was past his prime. For Hardy, mathematics is a young man’s game and he must have been prodded to write about mathematics for he was believer in doing things and not talk about it. His words might sound condescending but we get to get his mind as he expounds his reasons in the writing.

The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.

He alludes to the fact the mathematics in its purest form is nothing short of or even better than poetic lines of great depth. And his confidence in his own craft is telling and I couldn't help nodding positively reading the following lines –

I should say at once that my defense of mathematics will be a defense of myself, and that my apology is bound to be to some extent egotistical. I should not think it worthwhile to apologize for my subject if I regarded myself as one of its failures. Some egotism of this sort is inevitable, and I do not feel that it really needs justification. Good work is no done by ‘humble’ men.

Just like how a master poet playing with words brings forth great lines, mathematicians are makers of patterns made of ideas, patterns that are beautiful. He asserts that the patterns must be beautiful and if they aren't they are not worth pursuing. As examples of ideas that are simple yet profound and possessing inherent beauty Hardy describes Euclid’s proof of the existence of infinite primes and Pythagoras proof of irrationality. One cannot disagree. Even a person with no practice in mathematics can see the beauty of the proofs. I liked the lines that Hardy uses why reductio ad absurdum is so appealing for Mathematicians –

 The proof is by reductio ad absurdum, and reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game

The other aspect that Hardy argues and argues he does with rigor is the difference between pure mathematics and applied mathematics. Hardy rates pure mathematics highly and takes comfort with the fact that his and other real mathematician’s work finds no place in utility for mankind. It is useless in making life better, yes, he argues, but at the same time it does play no role in war as does the applied mathematics.

There is one purpose at any rate which the real mathematics may serve in war. When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as Bertrand Russell says, ‘one at least of our nobler impulses can best escape from the dreary exile of the actual world.

 Hardy must be forgiven for having not much foresight! His favourite line of mathematics – Number Theory –plays a crucial role in cryptography and other applications that do practical good as well as evil. Hardy belabours to get the distinction between pure and applied mathematics through and I found it at some places difficult to grasp the gist. Some chapters are pending further reading for better understanding.

Hardy ends the essays with one chapter which in substance touches the life he lived as a mathematician. He considers his collaboration with Littlewood and Ramanujan as his best works and his craft being bound with them.

All my best work since then has been bound up with theirs, and it is obvious that my association with them was the decisive event of my life. I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, ‘Well, I have done one the thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.’

He makes a case for himself and rightly so by acknowledging that he added something to knowledge (even if useless) and helped others do the same.

Reading Hardy’s defense for mathematics and its craftsmen I rued how wrong was it on my part for not taking mathematics seriously. Yes, I knew that mathematics is an art. I could appreciate its beauty (I despised shortening the subject to and calling it 'Max'). But still didn't excel and pursue it. Unlike other art forms like poetry or painting many of us have formal education for mathematics for many years. Still, I failed in mastering the art thus wasting an opportunity. But one can defend that software writing - beautiful software at that and debugging software also to be an art though Hardy would not put anything on par with mathematics! So, I at least have an opportunity by means of my profession to ace in some form of art.

Following Fish – Delightful Travelogue

Samanth Subramanian’s debut work, Following Fish, is a collection of essays which captures the essence of coastal India that is in some way or the other intertwined with fish. The author begins following fish cuisine from Kolkata in search of Bengal’s favorite hilsa fish and along the east coast eventually ending in Mangrol a town in Gujarat on the west coast. The people of Mangrol, even today survive by building boats for fishermen. The author traces the path of fish used in Hyderabad’s famous ‘fish treatment’, does interesting anthropology in Tuticorin in Tamil Nadu, which has a vibrant, largely Christian fishing community, gets high on toddy and karimeen in Kerala, tries hunting for the best fish curry in Mangalore, explores Goans’ fondness for fishing and how the beaches and art of fishing is being lost to overdose of tourism and tries finding the real Mumbaikars — the ‘Kolis’.

How did I, a vegetarian, and one who finds even the smell of fish repulsive get hold of this book which, at the outset, appears to be all about fish cuisine? I read excerpts from the book in the Lounge magazine. The writing about the Kerala toddy shops was lucid and made me realize that the book was not just about the fishes.

What I found interesting was that the book wasn’t just about fish and the delicious cuisine, but also about the people, the places, and their history. All this written in a very elegant manner yet with simplicity.

The most vibrant of all the essays to me was the one on the fishing community in Tuticorin. This essay is a good study of the anthropology of the fishing community which is largely Christian, thanks to Portuguese who set foot here in the sixteenth century and helped the paravas (a caste of fishermen) to overcome their rivals, the kayalar who followed the Islamic faith, thanks to Arabs who arrived in Tuticorin earlier. It was interesting to find overlapping aspects between the Christian faith as is currently followed by the community and the Hindus.  Church rituals include the aradhana, the valakappu ceremony for pregnant women, prostration before the church altar and even to the point of referring to the church as kovil.

I learnt a new word from this essay– syncretism — the fusion of two different belief systems.  In a very delightful way the author renders the life of the community as they live now and the disintegration of hierarchy which was prevalent till the previous generation.

The author’s experiences trying to get good toddy and tasty Karimeen in shops that dot Kerala’s highways made for a humorous read. The author’s auto-rickshaw rides reminded me of my own observations that auto -rickshaw drivers can be very forthcoming in lively conversations if you are willing to listen. The author comes across interesting characters who help him hunt the best toddy.

Another essay that I liked was that of the hunt for the best fish curry in Mangalore. I had visited Mangalore myself and felt that it celebrated a kind of laid back attitude which I liked the most. The shutters of most shops were down at noon and the roads were bereft of traffic. My thoughts on Mangalore were reaffirmed when Samanth Subramanian described the same attitude in Mangalore. He notes that there was a restaurant which had its shutters down indefinitely on the pretext of ongoing roadwork although the restaurant’s door was easily accessible.

Other essays also made for an interesting read, particularly the one on Mumbai and its Koli fishing community. It was interesting to know the origin of the name Mumbai (from Mumba Devi, the patron goddess of the Koli community). The essay on the dying art of fishing in Goa, thanks to excessive fishing and overdoing of activities to increase the influx of tourists has taken a toll on the ecology and the culture.

Overall, this is a delightful little travel book which was written the way I wanted and not a how-to travel guide but one in which people and places speak for themselves.

Dawkins' Next!

Richard Dawkins is one of my favorite authors. The passion with which he writes on evolution and defends it against any religious body deriding its significance cannot be missed. It is not just Richard’s writing that is fascinating and enlightening but his lectures and talks too are equally interesting. I am now eagerly awaiting his next book The Greatest Show on Earth. I expect it to be better than his masterpiece, The Selfish Gene. I am confident it would be.

Guns, Germs and Steel

Guns, Germs and Steel by Jared Diamond tries to answer a fundamental question: Why did history unfold differently on different continents. In dismissing any racial superiority of humans of one region over the other the author takes up the challenge of explaining the root cause of the difference that we find today. Since the end of the last ice age about 13,000 years ago different parts of the world have evolved in a very contrasting ways. From being hunter gatherers humans in some parts of the world evolved to non literate farming societies and in some other parts progressed into literate industrialized communities with metal tools. Some remained hunter gatherers. The book tackles in very engaging way the question of why and how peoples of Eurasia had the head start in the race of human progress and went on to conquer and dominate regions like Africa, Americas and Aboriginal Australia.

The book which has the subtitle, “a short history of everybody for the last 13,000 years”, tries to seek by means of rigorous analysis the ultimate factors that gave rise to proximate causes which in turn affected the course of history. It establishes that the environmental differences were the ultimate factor responsible for the diversification of the continents. The geography of Eurasia was such that it aided plant and animal domestication and farming. A community which starts food production rapidly evolves into a community of large, dense, sedentary, stratified societies. Owing to east/west orientation of continental axis of Eurasia the developments spread easier and rapidly as environmental conditions are more or less the same across the continent. Contrasting this with north/south orientation of Americas and Africa we find that variation in the geography hinders the spread of species and skills developed in one region to spread to other easily. Large population has the advantages that it can develop technology like guns and steel much more easily than distributed and isolated societies. Political organization and writing is the later logical outcome of it. There is also the other factor of germs having evolved from domesticated animals in Eurasia and its population over the years gaining immunity to those. And hence Eurasians armed with their guns, germs and steel went on to conquer other less blessed continents. Guns were no match to stone and primitive tools, germs carried by Eurasians unleashed epidemic of great proportions which resulted in disappearance of native communities in other continents in a limited time span. Steel and technology enabled Eurasians to establish their rule in new world in quick time and oppress the disadvantaged easily.

In the above paragraph, I have taken the liberty to put things in very broad terms what the author has painstakingly explained in the book with scientific rigour. I request that one should read the book to find out how and why various factors had affected the human history.

I found the book very engaging. The book which had me riveted with its initial chapter progresses with lot of intricate details which at times was difficult to read through. However this isn’t a novel and I appreciate the author for his efforts in narrating the history of a long timescale effectively. If you find the title and the subtitle inviting then I say, please indulge. You will not be disappointed.

The Kite Runner

Poignant. Brilliant. I cannot praise enough the first novel of Khaled Hosseini, The Kite Runner. The story is about love, loyalty, betrayal and redemption set in the backdrop of the cruelty of civil war that wrecks havoc in the life of Afghans.

As I read through, I felt that I was in the grip of a master story teller. I recommend it highly and I am eager to read his second novel, A Thousand Splendid Suns.

The Last Mughal

“At 4 p.m. on a hazy, humid winter’s afternoon in Rangoon in November 1862, soon after the end of the monsoon, a shrouded corpse was escorted by a small group of British soldiers to an anonymous grave at the back of a walled prison enclosure”

Thus starts the introduction paragraph of the book Last Mughal. The author later reveals that the corpse was that of state prisoner named Bahadur shah II, widely known as Zafar who is a direct descendant of Genghis Khan and Timur, of Akbar, Jahangir and Shah Jahan.

With such a riveting introduction to a book I was sure that the book was not a mere historical account about the Mughals and the 1857 revolution. And I was right.

The Last Mughal by William Dalrymple is an impressive body of literary work which brings history to life. The 1857 Uprising and the fall of the Mughals; Reading through the book, I was astounded by the sheer magnificence of the author’s dedicated research that had enabled him to write with such élan that would enable the reader to understand and interpret history. The book is not a catalogue of dates and events of the last days of the Mughal Empire and the Sepoy mutiny but is an evocative narrative of the fall of a dynasty which ruled for 300 or so years.

William has done a rigorous research by reading through archives which was untouched until he came and thus has written a whole new perspective in to the mutiny. And succeeds in explaining in a manner which is thoroughly enjoyable;
Inserted into the passages at various times are the actual letters that were written and exchanged by the characters. This makes reading an emotional act.

William brings out his uninhibited love for Delhi with great passion that it has made me wish for visiting the old historical city and picture the history for myself.

This book can easily be a reference to how to write history text books should be for schools. If history is told in manner how it ought to be it can be exciting and students can learn quiet a lot and mainly interpret it which I think is not done.

Made To Stick

Made To Stick by Chip and Dan Heath is delightful book about how to have our ideas and thoughts find its way in to the minds of our audience effectively. The key aspects of information that make them click are explained with loads of interesting anecdotes. The authors by dissecting ideas that have stuck strongly with the people bring out the essential ingredients of sticky ideas. There are six principles at work in making ideas last for long.

Simplicity: Ideas must be compact and at the same time have the ability to have a strong impact. The audience should be able to easily find the core message. The core should be profound as well. We shouldn’t bury the core by making our message complex.

Unexpectedness: When we are trying to get our point across to an audience we need to break their expectations. We should shatter their current understanding, surprise them and pull them in. Curiosity and interest needs to be created by filling out gaps in their understanding. This way we grab their attention.

Concreteness: Avoid abstractions. Concrete ideas tend to be in human understandable terms. While abstract thoughts leave the audience struggling to decode on what is being conveyed, concrete ideas let the crux of the matter quickly stick. The audience would understand the ideas better and remember them as well.

Credibility: People will be ready to hear you out only if your ideas have credibility. Give them an ample set of proofs that would enable them to asses for themselves the credibility of ideas.

Emotions: Our ideas need to touch audiences’ emotions. This way we can make them care for our ideas. The audience must feel, experience some kind of emotions when hearing our ideas.

Stories: If we wish that people act on our ideas, we need to present them with stories that let them picture themselves in the stories. This way people will try to act and try out things as was told in the stories. Stories enable us to imagine. They inspire us.

All these principles are explained in a lucid manner with lot of anecdotes that makes the intention of the book stick in the minds of readers! I enjoyed reading the book and I recommend it.

The Development Process

Steve Maguire's book Debugging the Development Process is an indispensable one to any engineer who is involved in software development task in any ways. Reading through the book, I was enlightened about the mistakes that I do and the wrong practices that software developers/leads and managers in general follow. I have resolved to put in practice his suggestions. And also its time that I dust Steve's other fine book Writing Solid Code from my book shelf and have it in my work desk for constant reference.

Ramanujan - The Man Who Knew Infinity

Roberts Kanigel's "The Man Who Knew Infinity" was an interesting read. The book is about Srinivasa Ramanujan’s incredible life and his Mathematics. The author details the life of the math genius in an accessible manner even for a reader who is remote to the kind of work Ramanujan excelled. The author succeeds in this because he does not dwell into the esoteric areas of Mathematics in which Ramanujan excelled but just makes a succinct reference to his works wherever necessary.

The story begins with an account of Ramanujan’s birthplace, Kumbakonam and his school education. Ramanujan faltered in all subjects but Mathematics. He stood apart from the rest in the way he worked out his favorite subject. After initial struggle in getting spotted as a boy with bundle of talent he does come to be recognized as a person with real mathematical skills. The significant recognition does not come from India but from England. Failing to find anyone in India who would properly understand him, he is advised to write to Cambridge and other places of repute. He writes to couple of distinguished Mathematicians in England for assistance only to be disappointed. But fate has it that he also writes to G. H Hardy. And Hardy responded with a keen interest in Ramanujan’s works. That was enough to spread the name of Ramanujan across the educated circle in South India. Hardy’s endorsement helps Ramanujan in getting rewarded with a scholarship. This enabled him to do his Mathematics at will not needing to care about his daily mores of his personal life, which had become a concern having been wedded at a young age. Hardy invites him to Cambridge and after initial apprehensions Ramanujan crosses seas against his caste traditions.

The author dedicates a chapter on Hardy, which gives a very good insight to the stuff that he is made of. The author does well in bringing out his love of Mathematics, penchant for Cricket, his atheism and much more. Then begins the engrossing passage of the book, Ramanujan’s life in Cambridge. Ramanujan finds in Hardy much-needed companion. Their ‘friendship’ and the work together would become a stuff of legend later. Though Hardy helped Ramanujan in finding his true self by enabling him to do his Mathematics, he failed to be friend at personal social level. The seven years that Ramanujan spends in Cambridge wrecks havoc to Ramanujan’s personal life. He remains totally unaware of most of the happenings back home. The straining of relationship between his mother and wife and many such painful events occur in India These and his staunch vegetarianism has him afflicted with Tuberculosis. But the work he does in Cambridge earns him a Fellow of Royal Society [FRS].

He returns to India as a FRS only to be pulled into the struggle of social life. His mathematical contribution remains at a minimal. Unable to cope up with pressures of life and unyielding health problems he passes away at a young age of thirty-two. The passage of his life towards the end makes for a sad reading. One can only wonder what could have been if only Ramanujan was healthy and lived for many more years.

I appreciate the author’s skill in writing the biography of one of enigmatic figures of India in a lucid manner. A very good read and I highly recommend it.