The adjective “sleepy” is still sometimes applied to Pondicherry, the former French colony on the south-east coast of India, but of course this is nonsense. Nowhere in India is sleepy, and Pondicherry is about as sleepy as a bank holiday in Brighton. Thousands of families stroll up and down its promenade, the Avenue Goubert, on a Sunday evening, and the crowd is only a little sparser at dawn the following morning, when men and women of all shapes and ages take advantage of the coolest hours of daylight to walk purposefully – or even jog – beside the sea as the sun rises out of it. The chaat, pizza slices and corncobs of the night before have been replaced by water bottles as the consumables to be held in the hand. Purging has followed feasting; austerity has replaced indulgence; but the promenade is hardly less full.

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On a visit last month, I decided that my own morning walk would take a different route. Rather than marching both ways along the prom, so that I twice passed the little Place de la République and the startling white memorial to the “combattants des Indes françaises” who died in the first world war, I would return to my hotel via the inland, acacia-lined streets of the old French quarter, and there escape the crowd and find some shade; by 8am it was already close to 30C.

The streets – the Rue François Martin, the Rue Saint Louis – were reasonably empty on the first two mornings. Across one of them, a couple of girls in Islamic dress played badminton. But on the third morning they were as busy as the promenade. Flocks of slender people in loose cotton clothes rode past on their bicycles or loped along in their sandals, and in one place sat cross-legged in rows that stretched from pavement to pavement: a crowd awaiting benediction and food. “Place your shoes over there,” said a steward, indicating a pile of them discarded by their owners. Eventually it became clear. This was a special day at the Sri Aurobindo ashram, which has been a prominent part of Pondicherry’s life for nearly a century, and the reason that people other than students of French colonial history have ever heard of the place.

According to another steward, supervising the queue for the meal tickets, the morning’s rituals celebrated the day the Mother arrived in the town for the first time. The year was 1914, and the woman in question was a 36-year-old member of the Paris bourgeoisie, Mirra Alfassa. She had a Turkish-Jewish father and an Egyptian-Jewish mother, and she sailed to Pondicherry with a French husband (her second) in pursuit of the occult – in particular the Bengali yogi and Indian nationalist Sri Aurobindo, who had moved to the colony, partly to escape the attention of the British Raj’s police. It was Aurobindo who called Alfassa the Mother.

In the world of the occult, their encounter ranks with Rolls meeting Royce, or Laurel bumping into Hardy: a historic moment that produced a famous partnership and, in their case, a brand of spiritual thought that has attracted followers ever since. It was an enduring version of what the west liked to think of as the mysterious east – high-minded and not at all threatening. Aurobindo wore Indian dress, a beard and long hair, but his education had included St Paul’s school in London and King’s College, Cambridge.

Their ashram attracted famous followers and influential friends. The eldest daughter of the US president Woodrow Wilson spent her last six years there. India’s first and third prime ministers – Jawaharlal Nehru and his daughter, Indira Gandhi – made several approving visits. But, beyond the beneficial effects of yoga and a vegetarian diet, the movement’s beliefs are hard to describe.

The Mother’s collected works run to 15 volumes. In Pondicherry I bought a brief anthology, The Mother on Herself, which announced some of her creed (“I belong to no nation, no civilisation, no society, no race, but to the Divine’’) as well as her aim “to establish an ideal society in a propitious spot for the flowering of the new race, the race of the Sons of God”. She had a religious tendency towards the initial capital – Truth, Harmony, Light, Love – and a belief in an all-powerful Supermind.

She wasn’t modest. She disclosed that her “complete identification” as the Universal Mother had taken place in 1914. In the same year, her intervention with the goddess Kali had prevented the German army’s capture of Paris. Later, 15 years before her death in 1973, a new realism seemed to have set in. She wrote: “It will be said of me: ‘She was ambitious, she wanted to transform the world.’ But the world does not want to be transformed except by a very long and slow process, so slow that the change cannot be perceptible from one generation to the other.”

The truer thing would be to say that the world, in her lifetime and the years since, has shown no inclination to be transformed in the way she and many others wanted, in terms of restricted human appetites and the reformed human soul. In most other ways, it has changed utterly. When the Mother died, India’s population was just under 600 million; this year it will reach roughly 1.35 billion, and by 2024 is expected to overtake China as the world’s most populous country. A visitor to Pondicherry 40 years ago would have seen half the number of people, perhaps many fewer, on his or her walk along the promenade; an expanding, prospering middle class can now afford more trips to the seaside. And of course, the seaside itself has changed: who could have imagined even 20 years ago the flotsam of plastic bottles, straws and bags that would float in with each tide?

Plastic waste is now a ubiquitous feature of the Indian landscape – the lining to every roadside, the shimmering surface of every garbage dump, the floater in every open drain. And there it was as usual, tangled in the verges and ditches of the lanes that lead to the Mother’s most extraordinary creation, the “international-universal” settlement of Auroville, which lies a 20-minute taxi journey outside the town.

Auroville was founded in 1968 as a sort of utopia: 2,250 acres of fields and scrubland with enough room for a population of 50,000, though so far only a 20th of that number have made a home there. It has cycle paths, solar kitchens, reforestation schemes, water-pumping windmills and two museums, and has attracted the support of several international organisations, including Unesco. Its most celebrated feature is a giant golden orb called the Matrimandir, the Temple of the Mother, which sits in the middle of a geometric pattern of lawns like an expensive but rather vulgar gift from another galaxy.

I walked a kilometre to the temple down a parched red-earth path from the visitor centre. It was very hot, and I was glad to take the bus back and sit in one of Auroville’s cafes under a fan and have coffee with a nice slice of walnut cake. Next door, a shop sold scarves, hats, soaps and other tasteful souvenirs. Garden servants raked leaves from the grass. Not a scrap of plastic could be seen. Was that Alan Bennett under his sunhat? I might have been enjoying an afternoon with the National Trust.

How odd to sit there, in this little Wiltshire in the east, and think how much more useful it was to gather up plastic, or abandon its production in the first place, than to try to achieve universal Harmony and penetrate the secrets of the Supermind.

• Ian Jack is a Guardian columnist