Incarnations

by Sunil Khilnani

  Another ancient mathematical puzzle Ramanujan solved at Cambridge—this time with Hardy—has to do with partitions. The partitions of a whole number are all the ways that a number can be added together using positive integers. For example, the number 4 can be partitioned in five different ways: 4, 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1. The number 5 can be partitioned in seven different ways. How many partitions would you guess 10 has? Forty-two. What about 100? Nearly 200 million is the answer. In other words, partitions grow extremely rapidly—and unpredictably. Once again, Ramanujan brought this chaos under control, creating a formula that predicted a number’s partitions with a remarkable degree of accuracy, and that got better and better as the numbers grew.

  If solving such long-standing problems was an extraordinary feat, the greater work would come two years later, in circumstances that had drastically altered.

  * * *

  I am extremely sorry for not writing you a single letter up to now. I discovered very interesting functions recently which I call “Mock” ϑ-functions. Unlike the “False” ϑ-functions (partially studied by Rogers), they enter into mathematics as beautifully as the ordinary theta functions. I am sending you with this letter some examples.

  Ramanujan was ill when he returned to Madras. Tuberculosis was the suspect, probably compounded by amoebic dysentery—treatable, had it been diagnosed. He was so enraged by his weakening body that he crunched up thermometers placed in his mouth. This letter, his last to Hardy, was composed in January 1920, on his deathbed. Enclosed with it were the bizarre series of functions that grip mathematicians today.

  While some valuable work was done to understand the mock-theta functions in the decades after Ramanujan’s death, it wasn’t until 1976, when the so-called “lost notebook” was found buried away in Trinity College’s Wren Library, that mathematicians really began to grasp their import. Perhaps the greatest breakthrough came only in 2001. It had taken more than eighty years to catch up with what Ramanujan had been doing.

  What mathematicians began to see was that mock-theta functions can be used to reduce different types of infinity down to small, simpler quantities. This allows the infinities to be relatively easily manipulated and studied. In recent years, astrophysicists have realized that when they peer into their models of black holes, what they are seeing, among other things, are Ramanujan’s mock-theta functions at work. String theorists, too, rely on mock thetas when trying to describe the most fundamental levels of physical reality.

  Ken Ono has often wondered how Ramanujan’s math might have developed if someone other than Hardy had answered Ramanujan’s letter—if a different mathematical mentor and collaborator had encouraged Ramanujan’s gift in other directions. And what if no one had written back to him? Westerners often remark on how lucky Ramanujan was to be discovered, but some scientists think that if he’d stayed in India he might have lived longer and done even more exceptional work, most of it perhaps still waiting to be understood.

  If his significance went largely unnoticed in Ramanujan’s own day, it’s not just that his formulae were gnomic: he was answering questions that wouldn’t be asked for decades, or even a century after he died, in areas of mathematics that people didn’t even know were important. It’s as if he described the alien inhabitants of a distant planet two generations before we knew the planet existed.

  Ultimately, much of what we would like to know about Ramanujan—how he worked, how he understood the meaning of his work, where it was going—seems to have been wiped away, like the notations on his slate. Or perhaps there were never any good answers. I think that even for Ramanujan himself, his process and purposes remained a mystery, so many motes of blown chalk suddenly forming constellations to those gifted enough to see them.

  32

  TAGORE

  Unlocking Cages

  1861–1941

  In the summer of 2015, I happened to arrive in Washington, D.C., on the afternoon on which the Supreme Court of the United States made same-sex marriage legal in all fifty states. By evening, as supporters of the verdict celebrated in streets and parks across the country, the White House glowed in the rainbow colors of the gay pride flag. As exhilarating as the historic moment was, what struck me more was what came afterward. A law that would have seemed radical a decade earlier settled almost instantly into the normal state of American affairs. Among liberals, political conversations moved on. It seemed to me a testimony to the deep roots of individual freedom in the United States.

  In India, by contrast, a person’s freedom to choose the life that he or she prefers is a liberty resting on fairly shaky ground. Section 377 of the Indian Penal Code, a relic of British rule that was upheld by the Indian Supreme Court as recently as 2013, decrees that a single act of same-sex love can land you in prison. And such constrictions are not just statutory, or only for homosexual relations. That Indians have to use the term “love marriage” to describe a freely chosen partnership between a woman and a man is a reminder that social and cultural pressures operate across the board to arrange the most intimate of human relationships.

  At the heart of this weakness, in marriage and in other realms of human choice, is the ancient caste order, which denied individuality in favor of assigned social roles. The idea of treating Indians primarily as members of communities was further entrenched by colonial legislation. Later, the social reform and nationalist movements that arose to challenge caste and empire were focused more on collective freedoms than on individual rights. And it was not as if economics could reel in the political slack: many of the economic processes associated with the rise of the individual in the West, such as a deeply ingrained system of personal property rights, began to take root in India only relatively recently, and even then they had to push against collectivist and socialistic currents.

  “The history of the growth of freedom,” the restless Bengali writer Rabindranath Tagore said, “is the history of the perfection of human relationship.” In a nationalist age when many of his compatriots were preoccupied with independence, Tagore, the first Asian to win the Nobel Prize for Literature, preferred to speak of freedom. As he roamed across cultural traditions and genres in a large, often agitated body of work (which included poetry, stories, novels, songs, drama, opera, memoirs, travelogues, and essays), Tagore returned repeatedly to this idea. He tested it, says Supriya Chaudhuri, a professor at Jadavpur University, against events, against experience, and against history and politics, to show “that political freedom is not worth a great deal if one can’t free oneself from mental bondage.”

  Tagore tried to create a space for individual choice that stood apart from imposed collectives, whether of traditional Indian institutions such as caste, religion, and patriarchal families; of imperial subjectdom; or of contemporary mass movements for nationalism. The dissolution of personal identity into cultish mass conformity even affected, in his view, the independence movement led by Mohandas Gandhi (38). Yet Tagore wasn’t a radical individualist; his conception of freedom was related to expressivity, connection, and the deepest human experience: love. Becoming who you are, he recognized, is not something you do on your own.

  Tagore was born in 1861 in Calcutta to an illustrious family, and published his first writings before the age of sixteen. A few years later, following a traumatic experience in love, his fiction began sensitively to explore the brutal subjugation of women at the heart of Indian family life. But women weren’t the only ones who suffered from the duties of family, society, caste, and religion. The subordination of individual hopes and choice to collective demands sent hidden ripples throughout an entire society. India’s growth was being stunted by the conformities of tradition.

  As political change swept through Asia and Europe in the early twentieth century, Tagore’s concern for personal freedom gathered intensity. Though passionately against imperialism, he homed in on a paradox of nationalism: new nations might destroy their civilizations’ distinct identity when replicating the patterns developed by the mod
ern European state. He saw, in places such as Japan, “the voluntary submission of the whole people to the trimming of their minds and clipping of their freedom by their government, which through various educational agencies regulates their thoughts, manufactures their feelings,” as he said in 1916. The result was an “all-pervading mental slavery” masked as national freedom.

  This critique of nationalism’s military and cultural modes made Tagore unique among anticolonial figures. Yet he didn’t always walk his own talk. As he shifted forms and avatars, he was given to self-contradiction, while some of his poetry (at least in its English translation) was misty enough to justify Bertrand Russell’s exasperated observation: “The sort of language that is admired by many Indians unfortunately does not, in fact, mean anything at all.”

  Still, Tagore’s arguments for the centrality of self-empowerment, or what he called atma-shakti, remained fairly sharp and consistent. The more that people were encouraged to express themselves openly and rationally, the more hopeful Tagore was that divisions might fall away, and that a universal, diversity-respecting humanism might arise. Such language might seem airy and archaic today, a little like the paintings Tagore made late in life. But to embrace it is to see something at the core of Tagore’s thinking, and something we now need.

  * * *

  Great advocates of individualism tend to consider themselves superior to the norm. Tagore, awash from birth in the advantages of multigenerational wealth and education, fits the profile. He came from one of the grandest clans of colonial Bengal, owners of marble mansions in Calcutta and vast zamindari estates in the eastern part of the province. Charles Dickens knew Tagore’s grandfather, Dwarkanath, as the “Oriental Croesus”; he was a man who, when visiting London, sat beside Queen Victoria to review her troops. A friend of Rammohun Roy (22), Dwarkanath was an entrepreneur and philanthropist at the center of the “Bengal Renaissance.”

  Tagore’s father, Debendranath, continued the cultural tradition. He was a leader of Roy’s rationalist religious reform movement, the Brahmo Samaj, and was a close reader of the Upanishads and of Persian poetry. He had thirteen children who survived beyond infancy, and he raised them in a lively and competitive, though socially conservative, household. His eldest son was the first Indian to join the elite Indian Civil Service. Another son was prominent in theater. The youngest child, Rabindranath, felt his historic importance from a very young age. He would later describe himself as containing from early on a perfect blend of cultural confluences (of Hindu, Muslim, and European worlds) that he wished the whole Indian nation would embody.

  Tagore was educated at home, mainly by tutors, and he never learned to like institutions. At seventeen, having published his first songs to acclaim, he went to England to study and enrolled at University College London. Although he didn’t stick it out to obtain a degree, he picked up a familiarity with British ways before returning home to a sociability he much preferred: the intellectual companionship he found with friends and family, particularly his sister-in-law Kadambari. Decades later, in his eighties and nearing death, he’d remember how the two of them would sit together in the hot afternoon reading the latest literary reviews from Calcutta, Kadambari fanning him gently. Their attachment was so deep that after Tagore’s father arranged his marriage, at the age of twenty-two, to an uneducated ten-year-old, Kadambari was undone. She took an overdose (possibly of opium, according to Tagore’s biographer Andrew Robinson). It was a suicide that would mark Tagore for life.

  Into his fiction, poetry, and polemic came a grave mood of yearning and a theme of injustice. The figure of the young woman married off against her will, fobbed off with the illusion that she will be happy and cared for, became a regular subject. Tagore wanted always to show that “without love, without a sense of mutual compassion and companionship, marriage is nothing,” Supriya Chaudhuri says. Consider the heroine in the devastating 1914 story “The Wife’s Letter,” in which a woman explains why she’s abandoning a household through which she’s long moved, invisible and unheard:

  My mother feared for this cleverness of mine; for a woman it was an impediment. If one who must follow the limits laid down by rule seeks to follow her intelligence, she will stumble repeatedly and come to grief. But what was I to do? God had carelessly given me much more intelligence than I needed to be a wife in your household.

  Restored to self-worth by the love of a maltreated young girl, the wife realizes that being unmoored and alone in the world, with the freedom to say so, is better than staying in a life in which one will “die inch by inch.”

  For Tagore, the patriarchal imprisonment of women was a crystallization of the way social conventions restricted all forms of individual desire, love, and experience. These conventions were a cage, or khancha, that would recur in his poetry and fiction, and would come to seem even more stifling than the political domination of the British. The “Hindu ideal of marriage has no regard for individual taste or inclination,” he complained in a 1925 essay, calling marriage “one of the most fruitful sources of unhappiness and the downfall of man.”

  In his last years, as Tagore glanced back at his life and his writing from early in the century, he spoke of having felt “the harsh touch of domesticity” in his own life. Marriage he saw as oppressive and constricting; but love he saw as essential, enabling “human beings to form truly emancipated relationships of interdependence,” says Chaudhuri.

  This collaborative view of the self, of freedom as interdependence, evolved, intriguingly, during a time of great personal loss. Within a period of six years, beginning in 1902, his wife, his father, and two of his favorite children all died. Meanwhile, he married off three of his daughters, barely in their teens. It was almost as if, once the series of deaths began, he was willing himself out of domestic life in one great rush—by demonstrating chilly indifference to his daughters’ own choices.

  Tagore’s characters, like their author, sometimes fail to embody his ideals. The social costs of upholding principle can be too steep, or tradition too seductively convenient. The Marxist critic György Lukács mauled Tagore for being an intellectual proxy for the European bourgeoisie, dismissing him as a pamphleteer whose characters were “pale stereotypes.” But even when Tagore’s novels were political arguments in mufti, the flaws and inconsistencies of his characters made him distinct in the Indian canon—and certainly more complex than doctrinaire.

  India’s literary traditions have the occasional Krishnadevaraya (14) or Allasani Peddana, writers who explored interiority and personal choice. Yet until late in the nineteenth century, individual lives were worth bothering about only when they were exemplary and morally improving. Tagore’s sympathy extended to the imperfect. For instance, in “The Broken Nest,” the story of a Kadambari-like young wife who falls in love with her cousin-in-law, a writer, the wife’s distracted husband, a struggling newspaper editor, could easily be a villain. Instead, Tagore gives this secondary character equal complexity, and a parallel heartbreak in the end. In Tagore’s world, fate follows the logic of specific choices, made by people with specific natures, encountering specific historical conditions; it has nothing to do with supernatural powers or caste destiny.

  That this emphasis was innovative in the early twentieth century reminds us how underdeveloped the idea of individuality was in Indian literature. Tagore’s contemporary, Chekhov, grew up with the interior fiction of Dostoyevsky and Pushkin, not to mention the work of Gogol, who was already so bored by Russian psychological inwardness in the first half of the nineteenth century that he wrote against it. In India, Tagore lacked such shoulders to stand on.

  So he became those shoulders for other writers—and for more than interiority. He also allowed his successors to envisage an Indian self that was broader than any one of the subcontinent’s many religious and cultural traditions. Tagore’s writing certainly has a strong sense of place—the natural landscape and culture of Bengal are intensely present and studied. But his cultural net was large, drawing in eleme
nts from other traditions, high and low. There are allusions to the Upanishads, Buddhism, the songs of the Bauls (a community of roving folksingers from eastern India), and more. In Tagore, such cultural elements inflect natures, but they don’t define them. Always, there is room for human idiosyncrasy.

  * * *

  One of Tagore’s most celebrated verses begins:

  Where the mind is without fear and the head is held high;

  Where knowledge is free;

  Where the world has not been broken up into fragments

  By narrow domestic walls …

  These are lines many Indian schoolchildren will recognize, and it’s as close as Tagore got to a political poem. Written in 1901, it ends with a wish for his country to awake to freedom. That would not take place until after Tagore’s death, but nevertheless his poem became well known during the years of the Swadeshi movement in Bengal. The nationalist agitation had begun during his period of personal loss: early on, perhaps as a distraction from his grief, he brought his many talents to the cause. He composed patriotic songs, among them one that became the national anthem of Bangladesh. (A few years later, he wrote what eventually became the Indian national anthem.) He invented festivals to instill brotherhood among his fellow Bengalis. He led marches. He used some of his family lands to try to develop a model rural community, inspired by the ideas of Armenian nationalists in Russia. And in his indignation, shared by many at British dismissals of Indian culture, he wrote in celebration of a glorious Indian past.

  His revivalist view of Indian history was considerably more expansive than some of his brethren’s. In part because of an infatuation with Japanese culture (though later he would reject and fear Japan’s nationalist politics), he cultivated for a time the idea of a mystical unity of Asian civilizations. Western humanism, and the Enlightenment, too, were gathered up and brought into his opening of the Indian mind. Yet as Tagore went broad, the Swadeshi movement narrowed. By 1907 it had become more of a Hindu movement, and its strategy drifted from public agitation toward clandestinely plotted violence. Nor was that violence exclusively directed at British targets: Bengal’s Hindus and Muslims also began to attack one another.