Lilly, who had gained the scientific establishment’s respect with his work on the human brain, became interested in dolphins in the Fifties, after performing a series of “inner-consciousness” investigations on himself in which he floated around for hours in salt water in an effort to block outside stimuli and increase his sensitivity.

His 1961 book Man and Dolphin was an international bestseller. It was the first book to claim that dolphins displayed complex emotions – that they were capable of controlling anger, for example, and that they, like humans, often trembled in response to being hurt. Some dolphin species, he said, had brains up to 40 per cent larger than humans’. As well as being our “cognitive equal”, Lilly speculated they were capable of a form of telepathy that was the key to understanding extraterrestrial communication. He also believed they could “teach us to live in outer space without gravity”. He also proposed that they could be trained to serve the Navy as a “glorified seeing-eye” (a theory that became the basis of the 1973 sci-fi thriller Day of the Dolphin, despite Lilly’s best attempts to halt production).

But Lilly did little to burnish his credentials in the early Sixties when he started exploring the psychological research possibilities offered by lysergic acid diethylamide (LSD). He took it himself, often while floating in his isolation tank. Lilly later pinpointed 1965, the year of the dolphin cohabitation experiment, as the year he came to “no longer regard the scientific viewpoint of total objectivity as the be-all and end-all”. It wouldn’t be wildly speculative to suggest that Lilly was – by today’s standards at least – not in quite the right frame of mind to be leading the dolphin project.

Looking back at his memories of the mid-Sixties in his autobiography, an impressionistic account in which he writes of himself in the third person (“He felt that he was merely a small microbe on a mudball, rotating around a G-star, two thirds of the way from Galactic centre…”), it is also apparent how removed he was from Howe’s work.

He writes: “In the midst of his enthusiasm he [Lilly] attempted to speak to [Howe] of his experiences.” Howe, in her early 20s, was not sympathetic. “If you want to do your experiments on solitude and LSD, please keep them in the isolation room. I am not curious or interested.”

Howe was among many keen young staff members he employed from the island. Only the bravest stayed with him any significant length of time; as Lilly noted in The Mind of the Dolphin (1967), the Tursiops (bottlenose) – chosen for study because its brain size was comparable to man’s – was larger and more powerful than most humans. They grew irritable and angry when mismanaged. Howe’s talent for communicating with the dolphins was exceptional and, as Lilly noted, her dedication was unmatched by anyone else in the faculty. “I will not interfere with that,” he wrote.

Still, he prepared the experiment. Following a week-long trial period, Lilly decided 10 weeks was the maximum time frame that both human and dolphin could survive comfortably in confinement. Objectives, regulations and a daily timetable were clear and precise. Howe’s aims were threefold: to make notes on interspecies isolation, to attempt to teach Peter to “speak”, and to gather information so that the living conditions might be improved for longer-term cohabitation.

On June 15 Howe moved in, her hair cut to a quarter-inch boy crop. All she needed was a swimming costume and a leotard for the cooler nights. The entire upstairs of the lab building and the balcony had been flooded with salt water 18in deep, which Peter could swim around in and Howe could wade through. A desk hung from the ceiling, and her bed was a suspended foam mattress that she later fitted with a shower curtain so that Peter’s splashes did not soak her through the night. She would live off canned food to minimise contact with outsiders.

“It was perfect,” she remembers today of her domestic dolphinarium. Early entries in her diary at the time reveal that, like a nervous new housewife, she made the best of things: “Cooking is fine. Cleaning is interesting… Each morning most of the dirt is neatly deposited at the foot of the elevator shaft. All I have to do is suck it up.” As for her companion, he spent “a good deal of his time in front of the mirror”, she noted. She was amused to find that during rare moments of contact with the outside world (mostly on the telephone) Peter talked “very loudly and in a competitive way” over the top of her.

Although he could be rambunctious, the archive footage of his lessons featured in the new BBC documentary reveal Peter to have been a curious, dedicated student. Lilly’s team had already established that dolphins could adjust the frequency of their squeaks and whistles to mimic human sounds, and claimed that during his time with Howe, Peter learnt to pronounce words such as “ball” and “diamond”, and to tell the difference between certain objects.

Howe was a creative, commendably patient teacher; when Peter struggled with certain sounds, particularly the “M” in her name, she came up with the inventive method of painting her face in thick white make-up and black lipstick so that he could clearly see the shape of her lips moving. “His eye was in [the] air looking at my mouth. There was no question… He really wanted to know: where is that noise coming from? What is the sound?” she remembers. “Eventually he kind of rolled over so that he would bubble [the ‘M’ sound] into the water.”

To those who lived and worked with Peter, his progress was perhaps clearer than it was to the outsider. The average viewer, on watching the BBC documentary, might conclude that the experiment was a failure. Kenneth Norris, an influential marine biologist, said of Lilly: “He started out as a capable scientist, but nothing he did was subject to measurement or truth, and that’s what scientists live by.” Experiments since 1965 have proved that dolphins have high levels of self-awareness and can understand human sign communication – but there is still little evidence that a dolphin language exists.

However, Peter’s linguistic progress was seemingly what kept Howe going when their relationship grew strained. Fed up and clearly exhausted by week three, she wrote at length about Peter whining and making loud noises night and day for no apparent reason: “I will do anything to break this… I lost my temper and nearly yelled at Peter… I am physically so pooped I can hardly stand… depression… wanting to get away… my mind is not all on the job.”

^{John C Lilly, pictured in 1977}

Lilly, responding to Howe’s feedback, recorded his concerns. “This is a dull and small area… Isolation effects showing,” he wrote. Howe’s diary of week five is predominantly concerned with a new issue: “Peter begins having erections and has them frequently when I play with him.” Her frustrated efforts to deal with his “sexual needs” and advances – which had become so aggressive that her legs were covered in minor injuries from his jamming and nibbling – had left her scared. “Peter could bite me in two,” she wrote. But she was reluctant to hamper progress, and, in a spirit of pragmatism, decided to take matters into her own hands. As the narrator in the documentary tactfully puts it: “Margaret felt that the best way of focusing his mind back on his lessons was to relieve his desires herself manually.”

Sex among dolphins is a “normal way to establish a bond”, White says. “Dolphins are mostly bisexual, sometimes heterosexual, sometimes homosexual, and quite frequent – eight to 10 times a day I’ve been told – so it’s a very different culture that we’re looking at.” Peter’s sexual advances wouldn’t surprise any marine biologist. But what astonished Lilly was the complexity of the way Peter and Howe’s relationship developed from thereon in.

“New totally unexpected sequence of events took place,” Lilly noted excitedly. “I feel that we are in the midst of a new becoming; moving into a previous unknown…” As Peter became increasingly gentle, tactile and sensitive to Howe’s feelings he began to “woo” her by softly stroking his teeth up and down her legs. “I stand very still, legs slightly apart, and Peter slides his mouth gently over my shin,” she wrote in her diary. “Peter is courting me… he has been most persistent and patient… Obviously a sexy business… The mood is very gentle, still and hushed… all movements are slow.” Today she talks about the whole experience philosophically: “It was very precious. It was very gentle… It was sexual on his part. It was not sexual on mine. Sensual, perhaps.”

Howe’s writing also reflects her increasingly protective feelings towards Peter, and at the end of her diary she admits that Peter’s attentiveness helped her overcome her “depression” and “fits of self-pity”.

In a neat romantic twist, it all ended happily for Howe. She left the lab to marry the project’s photographer, John Lovatt. Though dismayed to lose her, even Lilly was pleased: “Her intraspecies needs are finally being taken care of.” She never returned to work for him. Soon after the experiment, Lilly’s funding began to dry up, and with his second marriage in tatters he left to explore mystical interests in South America.

As for Peter, the lab’s vet Andy Williamson remembers his concerns as the experiment came to a close: “It was great [Howe] wasn’t going to be damaged… but as a veterinarian, I wondered about poor Peter. This dolphin was madly in love with her.”

The unexpected consequences of the experiment highlight one of the persisting problems with the “short-sighted” scientific approach to animal intelligence, says White. “We focus on language as the primary indicator of intelligence. Dolphins, like humans, are very sophisticated emotionally as well as intellectually. From an ethical standpoint, that’s what we should be looking at.”