Srinivasa Ramanujan and Lessons for Today's India

Today, April 26, 2020, marks the centennial death anniversary of Srinivasa Ramanujan, the self-taught math genius born into a poor family in Southern India in 1887 under British colonial rule, who conjured theorems and formulas in his short 32 years of life that continue to intrigue and challenge mathematicians to this day.

Srinivasa Ramanujan

The anniversary comes at a tragic time for India. Sectarian and police violence have claimed many lives, mostly Muslim, following the passing of a discriminatory Citizenship Amendment Act in 2019 aggressively promoted by Prime Minister Narendra Modi and his Hindu-Nationalist Bharatiya Janata Party (BJP). Indians of all faiths have been demonstrating against the law, although the coronavirus contagion has halted it for now. (But the pandemic has added its own macabre twist to the story. Reports are now emerging that right-wing fanatics are attacking and killing Indian Muslims for spreading the virus!) The original Citizenship Act of 1955 guaranteed citizenship to every Indian irrespective of religion, reflecting the aspirations of a secular, democratic nation. The amended bill favors all major religions of South Asia except Islam, a blatant discrimination against India’s 200-million Muslim community.

Remembering Ramanujan against today’s India offers lessons about the insidious ways by which bigotry and injustice can erode the soul of a nation and stifle the flowering of its geniuses.

Ramanujan would have withered away as a shipping clerk in Madras (now Chennai) had it not been for the patronage of an Englishman. In 1913, the same year that Rabindranath Tagore, another son of India, won the Nobel Prize for Literature, Ramanujan wrote a letter to the Cambridge mathematician G. H. Hardy to rescue him from oblivion. Trying to digest the 50 or so theorems included in the letter, Hardy realized he was dealing with a rare phenomenon. The mathematics seemed so sublime that Hardy was convinced “the results must be true, because, if they were not true, no one would have the imagination to invent them.”

Ramanujan's Letter to Hardy

G.H. Hardy

Hardy managed to bring Ramanujan to England through a grant, giving him an intellectual home at Cambridge where he flourished for five years, producing pioneering work in such branches as number theory and partition function that secured his reputation as among the greats of mathematics. The serendipitous discovery of Ramanujan’s “Lost Notebook” by Wisconsin University Mathematics professor George Andrew in 1976 that included calculations involving “mock theta functions,” 56 years after he worked them out in India, has added to the enigma and the otherworldly genius of Ramanujan. The late physicist Freeman Dyson (1923-2020) aptly summed up Ramanujan’s achievement: “That was the wonderful thing about Ramanujan. He discovered so much, and yet he left so much more in his garden for other people to discover … I have intermittently been coming back to Ramanujan’s garden. Every time I come back, I find fresh flowers blooming.”

From Ramanujan's Notebooks

Ramanujan’s theorems are now applied in fields ranging from particle physics and statistics to cryptology and computer science. His approximation for pi, the ratio of a circle’s circumference to its diameter, finds use in today’s fastest algorithms in computing the irrational number to trillion decimal places.

Ramanujan was lucky. (So was Tagore. Had not the Irish poet Yeats championed his work in the West, the Bengali poet would unlikely to have won the Nobel.) But for every Ramanujan who succeeded, how many Ramanujans must have died on the vine when the British ruled the Subcontinent for over a century? Colonial powers by their nature subjugate, exploit and massacre. But when the oppressors are one’s own leaders, what’s the excuse? Modi and his BJP passed the Citizenship Act to marginalize Muslims or drive them out of India. Such overt discrimination affects not only the target population but the entire nation, preventing potential Tagores and Ramanujans from ever seeing the light of day.

The human potential of India is incalculable. We get a sense of it by the disproportionate number of Indian American engineers and CEOs keeping hi-tech companies humming right here in Silicon Valley. Brain drain from India and other countries will continue so long as the West offers better opportunities to immigrants. While India cannot provide such opportunities for all, passing discriminatory laws against a segment of its population diminishes the nation and shackles its geniuses, be they Hindu, Sikh, Christian or Muslim. When a government becomes tyrannical, the creative vitality of its people seeps away as from cut flowers in a vase.

Time Freezes in ‎Punxsutawney on Groundhog Day

(“Groundhog Day,” starring Bill Murray and Andie MacDowell, was released a quarter-century ago today. On this Friday, the 2^nd of February, 2018, the only celebrity groundhog of the universe, Punxsutawney Phil, has seen his shadow, predicting another six weeks of winter. But what accounts for the timeless appeal of the movie, for its enduring charm? I think the reason is clear: Time. The movie explores the mystery of time subtly yet forcefully, mixing humor with depth that forces the viewer – through the experience of the arrogant and narcissistic weatherman Phil Connors who is trapped in a time warp and finds himself living in the same Groundhog Day over and over again - to confront mortality, life, love, loss, priority, memory, leading ultimately to redemption and enlightenment. The sign of a timeless movie is not just that newer viewers also become fans but that repeat viewers find something new every time they see it again.)

What if there isn’t a tomorrow? There wasn’t one today!

Think of the myriad ways by which we describe time: time flies, time crawls, time stands still, time loops, time is finite, time is infinite, time is money, time dilates, the arrow of time, cyclical time, circular time, linear time, non-linear time, geological time, atomic time, fullness of time, texture of time, fleeting time, recursive time, in the nick of time, the gift of time, the labyrinth of time, and particularly in Silicon Valley, billable time.

Probably no metaphor is used more extensively to describe an entity in literature and science than time. Listen to the echo of time in “To Be Or Not To Be.” Proust spent decades “In Search of Lost Time.” For Muhammad Ali, “The man who views the world at 50 the same as he did at 20 has wasted 30 years of his life.” To Thoreau, “Time is but the stream I go
a-fishing in.” From Julia Abigail Fletcher Carney:  So the little moments,/Humble though they be,/Make the mighty ages/Of Eternity. Rabindranath Tagore: "Floating on the sea of time, yet cannot grasp a drop of it!"

Physicist Richard Feynman: “A positron is an electron going backwards in time.” How about ‘forever and ever’ time? Physicists who won the 2017 physics Nobel Prize (Thorne, Weiss, Barish) were cited for “detecting gravity waves, predicted by Albert Einstein a hundred years ago, that came from a collision between two black holes. It took 1.3 billion years for the waves to arrive at the Laser Interferometer Gravitational-Wave Observatory detector in the United States. The LIGO registered the wave as a tone nicknamed the ‘cosmic chirp.’”

And if entanglement in space from quantum mechanics is not strange enough, how about entanglement in time?

So what do you want out of life?

The best way to honor the gift of life is to honor the gift of time …

The night sky is dense with stars. A new one seems to bloom every few minutes, making the dark domed garden even more inviting. But it is not the stars that hold me in their spell.

It is the trees.

I am in Chittagong, in the city of my birth by the Bay of Bengal in Bangladesh, almost eight thousand miles away from my ‘naturalized’ home in San Jose, California.

The mango and the betel nut saplings that my father had planted a half-century ago are now taller than the three-story building of my adolescent years. Rustling and dreamlike, they speak to me in a voice so real and with such urgency that I have to grip the railing from trembling.

“What have you done with your time?” they ask. “You saw us in our infancy Now the stars are within our reach. What have you done with the years gone by?”

I scan my life for an answer, memory guiding me down a path of light and shadow. Experienced life’s inevitable ebb and flow. Father passed away a decade ago after fighting diabetes for years. Children grow up, move out. Mother confined to a wheelchair as time takes its relentless toll on this irrepressible woman.

Wife and I continue working, retirement not in sight for economic reasons, even though we are advanced in years.

But ‘summing up’ isn’t what these animated trees are interested in. They want to know if I have used my time well. They are not interested in fame or wealth, neither of which I have, but whether I have honored time, given it the respect it deserved. They want to know if I was able to coax from it the ability to connect the dots that lay scattered about me, each a milestone of sorts in search of an elusive meaning.

So I really don’t know if I have used my time well in six decades. The truth and the tragedy are that I probably never will!

Do you ever have déjà vu, Mrs. Lancaster?
I don’t think so, but I could check with the kitchen.

Do you know what today is?
No, what?
Today is tomorrow. It happened.

What would you do if you were stuck in one place and every day was exactly the same,
 and nothing that you did mattered?

That about sums it up for me.

Do you ever have déjà vu?

Didn't you just ask me that?

Although it is winter, the night is mild and redolent of Bay of Bengal a few miles away. A preternatural silence has enveloped the bustling port city and the occasional tinkle of a rickshaw at the edge of my consciousness only deepens this silence. I find myself caught in a time warp that seems to extend beyond the Milky Way. My wife is asleep in the room where she slept as a bride over three decades ago, unaware of the ghosts of yesteryears crowding me. A breeze rustles the mango leaves and sways the betel nut trees and I hear their insistent question: “What have you done with the gift of time?”

At last I give up. “I don’t know,” I whisper.

Sometimes, people just die.

Not today.

How about you? What do you want?

What I really want is someone like you.

I think you're the kindest, sweetest, prettiest person I've ever met in my life. I've never seen anyone that's nicer to people than you are. The first time I saw you... something happened to me. I never told you but... I knew that I wanted to hold you as hard as I could. I don't deserve someone like you. But if I ever could, I swear I would love you for the rest of my life.

It's beautiful. I don't know what to say.

I do. Whatever happens tomorrow, or for the rest of my life, I'm happy now... because I love you.

It's so beautiful!... Let's live here.

We'll rent, to start.

Phil Connors gets caught in a time warp and finds himself slowly turning mad. He embraces death but the warp keeps delivering him to life’s shore. Slowly the scales of solipsism and arrogance fall from his eyes and by the time he comes free of the “same old, same old,” he has found the meaning and purpose of his life.

If only the rest of us are as lucky!

Apple's Ascendance

For Steve Jobs, each Apple product - iPod, iPhone, iPad, iAnyThing - must not only be a marvel of technology but also a work of art. This confluence of function, design, aesthetics, software and hardware has captivated consumers around the globe and transformed Apple into the most valuable technology company in the world.

At the recent Worldwide Developer Conference in San Francisco, the visionary chiel of Apple unveiled another service – iCloud - that is likely to increase the company's lead over competition.

After some failed attempts, Apple has perfected the technology to eliminate the need for manually synchronizing content to smart devices. iCloud will allow users to store content - music, photos, backups, contacts, calendars, email and ebooks - on Apple’s remote servers (“cloud”) and have it automatically pushed to their iPhone, iPad, iPod and Mac or PC via WiFi.

iCloud is free. Each user gets 5GB of free storage, more than plenty for most consumers. More storage will require an annual subscription.

The term “automatically” is a critical differentiator. Apple users will not need to manually upload content to iCloud; it will happen, well, automatically. This is where Apple leapfrogs over its competitors. Both Amazon and Google have announced their own cloud services but they require manual uploading, a boring and time-consuming process that looks primitive compared to Apple’s.

The only “restriction” for iCloud to work seamlessly is that the devices will have to belong to the Apple ecosystem, that is, all the ‘i’ devices across the Apple universe. The company has ensured it by integrating iCloud technology into its operating systems – the iOS for the iPhone, iPod Touch and iPad, and the Mac OS for its laptop and desktop computers. All Apple devices will be able to “talk” to the cloud. Users will be able to move content to and from the cloud no matter where they are, as if they are communicating with their local hard drives. iCloud will also automatically backup all your mobile devices.

Will this lock current and future users into Apple products? Steve Jobs certainly hopes so. iCloud will become available in September with the release of iOS 5.

What does iCloud do to the current state of consumer technology? It profoundly disrupts it. As Jobs said: “We’re going to demote PC and Mac to just be a device. We’re going to move the digital hub, the center of your digital life, into the cloud.” The Post-PC world is upon us.

One company that Apple has completely overshadowed is Microsoft. Every time Apple releases a product or a service, Microsoft comes across as a plodding behemoth and a weak imitator. When Apple launched its wildly successful iPod in 2001, Microsoft followed with Zune in 2006 but withdrew it from the market in 2010. It was a no-contest: Zune was inferior to iPod in every way. When Apple introduced the iPhone in 2007, it took Microsoft 3 years before releasing a competitive product, Windows Phone 7. But the Microsoft phone is a distant third after the iPhone and Google’s Android phones. Microsoft’s purchase of Skype in May for $8.5 billion has left many industry analysts scratching their heads.

In May of 2010, Apple surpassed Microsoft as the world’s biggest technology company based on market value, after Apple almost went out of business in 1990. Apple now has a market value of about $320 billion, more than the combined value of Microsoft ($200 billion) and Intel ($115 billion)! The only other company in the world that has a greater market value is ExxonMobil ($390 billion), the oil company. Industry experts are speculating that Apple may overtake ExxonMobil in the near future.

While for the last 10 years, Microsoft stock has been stuck at about $25 a share, Apple’s stock soared from $11 a share in 2001 to its current value of $330, a rise of over 3000%!

The bulk of Microsoft’s revenue continues to be generated by its two cash cows, the Windows operating system and the Office suite. But as the digital hub moves from the PC to the cloud, and as the iPad relentlessly cuts into the sale of Windows PCs, the top technology company of the ‘80s and the ‘90s appears to be six or seven steps behind Apple.

There is no one with the vision and business acumen of Steve Jobs at Microsoft. Bill Gates, his closest competitor, left Microsoft in 2008, and while the current CEO Steve Ballmer is a talented manager, he is no Bill Gates and certainly no Steve Jobs. Recently, when a respected money manager asked Steve Ballmer to step down and pass on the torch to someone else, Microsoft stock immediately went up. Microsoft sorely needs a new vision and a new style of thinking at the top to regain the glory of its yesteryears.

Apple is on a roll. How long can this last? Just as empires rise and fall, so do technology companies. Today’s colossus is tomorrow’s also-ran. Yet Jobs seems to have found a way to keep reinventing Apple. He is currently battling pancreatic cancer but the vision he has laid out for his company and the creativity he has unleashed among his engineers will probably help Apple continue its dominance in mindshare and market share for several years to come.

As our gadgets become smarter and smarter, do we run the risk of becoming dumber and dumber? After all, if our smart devices can do our work for us and even think for us, what is left for us to do other than to scroll screens and push buttons for titillation and entertainment? Sure, we can create documents and post opinions and search databases and look up references and be connected to each other and to the cloud 24x7, but will our creativity be sucked out of us in that mode of mostly passive consumption? Smart devices may give us instant access to the world’s storehouse of knowledge but unless we set aside time for reflection and assimilation, it is difficult to see how intelligent gadgets can help produce a Fermi or a Tagore.