These transcendent, haunting images taken by photographer Andrew Sutton in the waters of the western Indian Ocean come close to understanding something of the magnificent and enigmatic sperm whale, an animal which still remains fairly unknowable to us, for all that we have exploited it for 500 years.

Don’t tell the other cetaceans, but I think sperm whales are the most beautiful mammals on the planet.

For millennia they have swum in every ocean, occupied only with their physical and cultural selves. They still hang there, dreaming. And according to the scientist Hal Whitehead, we may even have an inkling of those dreams.

Whitehead, who began his work observing sperm whales off Sri Lanka, has done much to advance our knowledge of why, as much as how, these creatures exist.

He wonders why they have such big brains and if they think about their existential existence. Might they, like us, have even evolved notions of religion to explain their life on earth?

These are wild ideas, I know, but these wild animals encourage them. Sperm whales turn you a little crazy. They go beyond the superlatives – the biggest brain, the deepest diving, the largest-toothed carnivore – to become something else. Theirs is a matriarchal society governed by loyalty and a sense of collective individuality in which their system of communicative clicks has an almost extrasensory role. Whatever they are, they are linked by sound, and their selves.

Imagine yourself in association with such an animal; to place yourself in physical proximity with her. This is what Sutton’s photographs do. Blue Planet Live might get us close to the action.

But there is something contemplative and, I would suggest, even spiritual about a deep, still photograph that speaks of these deep, still denizens. Diving with Sutton, I have spent time in the water with these animals in Sri Lanka, and the Azores. We’ve been echolocated by them. We’ve even seen them being hunted by killer whales.

Yet for all these close encounters, we are left with a sense of distance – even when a whale is barely a metre away (on one occasion in the Azores, we were nearly squashed between a pair of them). The water connects us physically, but disconnects us, too. There’s a gulf of natural and human history between us.

It is one of the many ironies about the great whales – whom we nearly reduced to extinction in the last century – that, as huge as they are, so few of us have seen them. That, as big as they are, they now rely on diminutive humans for their continuance.

Sri Lanka has been seen as a possible location for the original Eden, although its recent history has hardly borne that out. Whale-watching from the island has only recently taken off, after the end, in 2009, of the war with the Tamil Tigers (the Liberation Tigers of Tamil Eelam, or the LTTE), which restricted tourist access to its waters.

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Trincomalee, on the eastern coast of the island, close to the Jaffna peninsula, was particularly affected. Now it is a magnet for whale-watching, as is the southern tip of Sri Lanka and the rapidly developing resort of Mirissa, where there have been accusations of harassment of whales.

The discovery of a third cetacean hotspot on the island is now presenting new problems. Kalpitiya, a peninsula on the west coast of Sri Lanka, has been a kite-surfing venue for a decade or more. The presence of frequently-seen megapods of balletic spinner dolphins – up to 2,000 strong – has also drawn tourists. It would be hard to deny anyone the joy of these cetaceans – a single dolphin’s trajectory recreated here, like the phases of the moon, in a composite image.

Meanwhile, manta rays glide through the same warm waters.

Since 2010, the Sri Lankan marine biologist Ranil Nanayakkara has been observing unusually large pods of sperm whales off Kalpitiya from February to April. On one occasion, he counted at least 300 animals in one group.

Unlike western nations, Sri Lanka has never had a culture of using whales as a resource – until now. The whales that come to this part of the Indian Ocean each spring have hitherto escaped unwanted human attention. Indeed, sperm whales possess their own culture which has seen this sea as a safe place in which to forage, socialise, mate, or even to sleep.

Sutton is working with Vanessa Williams-Grey of Whale and Dolphin Conservation’s (WDC) Project Blueprint to mitigate the effects of human-whale interactions in Sri Lanka. In 2011 there only involved three or four whale-watch operators along Kalpitya’s 50km stretch of coast. When I lasted visited, in 2017, there were 20. Now there are at least 90.

WDC’s solution is to set up workshops for responsible whale-watching with local operators and to discuss ways that the fishing community can work around whales. In that process, they’re learning new contexts. Nanayakkara spoke to some of the elder fishermen, who have been working the waters for decades. They recall that the Kalpitiya peninsula was “fiercely controlled” by the LTTE who monitored catches. Breaking these laws risked a death sentence.

Ironically, a violent war helped preserve a fragile peace for these animals. One fisherman observed that the komoduwa – the sperm whales – “appeared to get stronger in numbers, indeed even stronger than before the war when there was more unregulated fishing in the area”. Others recall that before the widespread use of outboard motors, the whales were gathering in such dense numbers that the fishermen found it difficult to get out to sea and back.

An Edenic scene to conservationists – waters filled with whales – is a nuisance if you’re trying to catch fish. “You could walk on water, across their backs, moving from group to group,” said one fisherman, as if “they could form a bridge away from the troubles”. The widespread use of outboards solved a problem for the fisherman, but created a new one for animals whose principal sense is sound.

More urgently, Nanayakkara notes that now international film crews and mass tourism are affecting the whales’ behaviour – especially with increasing use of drones.

“This is the new threat for the animals,” he says. “When once they were inquisitive and came to the boats, now they spy-hop” – sticking their head perpendicularly out of the water to look for possible threats – “and shy away from the mosquito-sound of the speedboats.” It remains to be seen whether conservation and awareness schemes can address these issues.

Sutton, who has been photographing Sri Lanka’s whale population for a decade, has noted “big changes in the animals’ behaviour” with “constant spy-hopping when you are close”. With a new 60-bed hotel being built to house visitors, things are set to become less restful for Kalpitiya’s cetacean guests.

We may not know what sperm whales dream of, but I know what I dream about. They’re big and grey and I hope they can go on dozing, down there in the big blue sea.