The Ganges River begins in the Himalayas, roughly three hundred miles north of Delhi and five miles south of India’s border with Tibet, where it emerges from an ice cave called Gaumukh (the Cow’s Mouth) and is known as the Bhagirathi. Eleven miles downstream, gray-blue with glacial silt, it reaches the small temple town of Gangotri. Pilgrims cluster on the rocky riverbank. Some swallow mouthfuls of the icy water, which they call amrit—nectar. Women in bright saris wade out into the water, filling small plastic flasks to take home. Indians living abroad can buy a bottle of it on Amazon or on eBay for $9.99.

To hundreds of millions of Hindus, in India and around the world, the Ganges is not just a river but also a goddess, Ganga, who was brought down to Earth from her home in the Milky Way by Lord Shiva, flowing through his dreadlocks to break the force of her fall. The sixteenth-century Mogul emperor Akbar called it “the water of immortality,” and insisted on serving it at court. In 1615, Nicholas Withington, one of the earliest English travellers in India, wrote that water from the Ganges “will never stinke, though kepte never so longe, neyther will anye wormes or vermine breede therein.” The myth persists that the river has a self-purifying quality—sometimes ascribed to sulfur springs, or to high levels of natural radioactivity in the Himalayan headwaters, or to the presence of bacteriophages, viruses that can destroy bacteria.

Below Gangotri, the river’s path is one of increasing degradation. Its banks are disfigured by small hydropower stations, some half built, and by diversion tunnels, blasted out of solid rock, that leave miles of the riverbed dry. The towering hydroelectric dam at Tehri, which began operating in 2006, releases a flood or a dribble or nothing at all, depending on the vagaries of the season and the fluctuating demands of the power grid. The first significant human pollution begins at Uttarkashi, seventy miles or so from the source of the river. Like most Indian municipalities, Uttarkashi—a grimy cement-and-cinder-block town of eighteen thousand—has no proper means of disposing of garbage. Instead, the waste is taken to an open dump site, where, after a heavy rain, it washes into the river.

A hundred and twenty miles to the south, at the ancient pilgrimage city of Haridwar, the Ganges enters the plains. This is the starting point for hundreds of miles of irrigation canals built by the British, beginning in the eighteen-forties, after a major famine. What’s left of the river is ill-equipped to cope with the pollution and inefficient use of water for irrigation farther downstream. Below its confluence with the Yamuna River, which is nearly devoid of life after passing through Delhi, the Ganges picks up the effluent from sugar refineries, distilleries, pulp and paper mills, and tanneries, as well as the contaminated agricultural runoff from the great Gangetic Plain, the rice bowl of North India, on which half a billion people depend for their survival.

By the time the river reaches the Bay of Bengal, more than fifteen hundred miles from its source, it has passed through Allahabad, Varanasi, Patna, Kolkata, a hundred smaller towns and cities, and thousands of riverside villages—all lacking sanitation. The Ganges absorbs more than a billion gallons of waste each day, three-quarters of it raw sewage and domestic waste and the rest industrial effluent, and is one of the ten most polluted rivers in the world.

Indian governments have been trying to clean up the Ganges for thirty years. Official estimates of the amount spent on this effort vary widely, from six hundred million dollars to as much as three billion dollars; every attempt has been undone by corruption and apathy. Prime Minister Narendra Modi, elected in May of 2014, is the latest to try. Modi and his Hindu-nationalist Bharatiya Janata Party, or B.J.P., campaigned on promises of transforming India into a prosperous, vibrant modern society, a nation of bullet trains, solar farms, “smart cities,” and transparent government. Central to Modi’s vision is the Clean India Mission—Swachh Bharat Abhiyan. He insists that rapid economic development and raising millions of people out of poverty need not come at the cost of dead rivers and polluted air. So far, however, the most striking feature of his energy policy has been the rapid acceleration of coal mining and of coal-fired power plants. In many cities, the air quality is hazardous, causing half a million premature deaths each year.

Two months after Modi was elected, he announced his most ambitious cleanup initiative: Namami Gange, or Obeisance to the Ganges. As evidence of his capability, Modi points to the western state of Gujarat, where he served as Chief Minister from 2001 to 2014, presiding over impressive economic growth. The Sabarmati River, which flows through Ahmedabad, the largest city in Gujarat, was given an elegant tree-shaded esplanade, where residents now walk their dogs and take the evening air; still, it remains one of the most polluted rivers in India.

Modi is better known for his long association with the radical fringe of Hindu nationalism than for good-government initiatives. Born into a low-caste family (his father sold tea at a railway station), he was just eight years old when he began attending meetings of the Rashtriya Swayamsevak Sangh, the mass organization that is the most aggressive face of Hindu-nationalist ideology. In his twenties, he became a leader of the R.S.S.’s student affiliate, and soon after he befriended another leading activist, Amit Shah, who became his most trusted aide in Gujarat.

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In 1990, Modi, already recognized as a future leader of the B.J.P., was one of the main organizers of a protest pilgrimage from Gujarat to the town of Ayodhya, in the northern state of Uttar Pradesh. According to legend, Ayodhya was the home of the god Rama, and the protesters demanded that a Hindu temple be erected on a site occupied by a sixteenth-century mosque. In 1992, Hindu mobs converged on Ayodhya. They tore down the mosque, prompting nationwide riots, in which two thousand people died. Ten years later, when Modi was Chief Minister of Gujarat, Hindu pilgrims made another visit to Ayodhya. As they were returning, Muslim mobs set their train on fire and fifty-nine people were burned alive. In reprisal, more than a thousand Muslims were killed, while the police stood by. Modi was widely accused of indifference, even of complicity, and, although he was later exonerated by the Supreme Court, he was denied a U.S. visa for a decade.

In 2014, Modi won a landslide election victory. Voters were tired of corruption, and Modi, a charismatic orator and an astute user of social media, promised to eradicate it. The business community clamored for deregulation. Young Indians were desperate for jobs. The Nehru-Gandhi dynasty had exhausted its political appeal, and its choice for prime minister, Rahul Gandhi, the grandson of Indira, was a feeble campaigner, no match for Modi’s dynamism.

For the most part, Modi did not need to appeal to Hindu-nationalist passions. But his promise to clean up the Ganges plays directly into India’s charged religious and caste politics. Two problems are paramount. One is pollution from the tannery industry, which is centered in Kanpur, roughly midway along the river, and is almost entirely Muslim-owned. The other is sewage from Varanasi, two hundred miles downstream—an ancient city, considered the spiritual center of Hinduism, where the river is effectively an open sewer. Both cities are in the state of Uttar Pradesh, which has a population of two hundred and fifteen million and is central to Indian electoral politics. It is also notorious for extreme poverty, rampant corruption, rigid caste divisions, and communal violence, in which most of the victims are Muslims. At least half the mass killings recorded in India in the past quarter century have occurred in Uttar Pradesh.