Genovés called his craft Acali, meaning "house on water", and envisioned the experiment as a study in human behaviour and gender politics, but tabloid journalists were quick to dub it "the sex raft".
There was indeed sex, and mutiny, and even a murder plot.
To finance the project, Genovés inked a deal with a Mexican TV station, and the newly rediscovered footage forms the backbone of an extraordinary documentary.
Word had reached Edna Reves - a 32-year-old Israeli anaesthetist working in one of Tel Aviv's biggest hospitals - that the expedition was looking for a doctor, specifically a female one. A divorcée who was in a new relationship with a naturopath, she nevertheless applied.
"I always liked the sea," she tells me today. "I am not a fast swimmer but I can go for an hour in the Med."
I don't doubt it. The now 78-year-old Reves is an on-call paramedic, who has honoured our interview appointment despite having tended to overdoses since five o'clock this morning. Twentysomethings have flaked out over less, I note. "I'll retire when I'm dead," she chuckles.
Reves's application was successful, and on May 11, 1973 she was among the 10 volunteers who met for the first time in Las Palmas in Gran Canaria to board a 24 x 39ft motorless "sardine can" that would drift across the Atlantic to Mexico for some 101 days.
Distractions such as books and magazines were forbidden, and sleeping quarters were close, and co-ed. Participants had to fill out intimate questionnaires detailing who they found attractive and the frequency with which they masturbated."
"I was always completely honest out of respect for the experiment," says Reves. Others would not be so scrupulous - including Genovés himself.
In his floating laboratory, Genovés recruited women to positions of seniority. A female professional diver from France was responsible for monitoring the raft's underbelly. A Swedish sailor named Maria Björnstam was captain. The men performed menial tasks.
"Santiago's hypothesis was that the men would rise up and take over," Reves tells me.
The reality proved to be somewhat different. Bonhomie soon gave way, not to sex-starved savagery, but boredom. Reves tended to her fellow passengers' seasickness and stage fright-induced constipation.
Accordingly, a frustrated Genovés stepped up his manipulations, using moves that would find their way into the reality TV producer's playbook decades later. He tabled a (successful) motion that the group should spend a day naked.
"He decided everybody must be alone for one hour with everyone else of the opposite sex, on lookout," says Reves, who reports having had "a little something" with two raftsmen: a Japanese photographer called Eisuke Yamaki, and Charles Antoni, owner of a Greek restaurant in Cambridge.
She says these couplings were less torrid trysts, more gestures of sunny solidarity - albeit gymnastically accomplished ones.
"It was complicated to have sex on the raft because everyone could see you. Maybe if two of you were on the lookout together and you were a little bit quick, then it was possible, but it was difficult because you had to use both of your hands for steering."Reves refused to rise to Genovés' frequent prurient provocations.
"I wasn't ashamed then and I'm not ashamed now," she tells me, noting that she had refused Genovés's sexual advances early on.
In signing up, Reves had defied her father's command that she should stay in Tel Aviv for her daughters, who were four and nine at the time. On board, she missed them terribly, and was overjoyed when an amateur radio operator in Tel Aviv made contact and arranged to put Reves's daughters on the line, but Genovés cut short the exchange so that he could wax lyrical on his anthropological findings.
"Santiago was so totally egotistical. He wouldn't let women do their jobs," she recalls.
A decisive moment came as the raft drifted towards the path of an Atlantic cyclone. Instead of heeding the advice of Captain Björnstam that it would be unconscionable to continue, the macho Mexican deposed her - declaring himself captain of the vessel.
This mutiny prompted a depression in Björnstam that would have the producers of today's reality shows reaching for their compliance manuals.
Genovés panicked in the storm and had a crisis of confidence. "I realised that the only one who has shown any kind of violence or aggression is me - the man who tried to control everyone," he later wrote.
He became ill, with what Reves says was appendicitis or inflammatory bowel disease (though others on the raft thought he was making it up).
As the raft's doctor, it fell to her to tend to Genovés. Though never one to harbour a grudge, she admits that she enjoyed the relative silence. "The illness finally made him a little bit quiet," she says.
Meanwhile, unknown to Reves, her crew-mates huddled on deck, concocting ever more lurid plans to do away with their tormentor. One scheme involved distracting Reves for long enough to steal medical supplies and administer Genovés with a lethal injection.
"I saw we had it in us to do something terrible for survival," admits Fé Seymour, a haunted former crew member, in the film.
Reves takes the revelations with a pinch of salt. "I think when you're angry and you talk about it, it's like going to a psychiatrist or a therapist," she tells me. "But I don't think they were serious."
In the end, they stopped short of murder, and the Acali docked safely in the island of Cozumel, the participants shocked to discover the tabloids' salacious "sex raft" narrative.
On dry land, a revivified Genovés wrote a book, Acali, which repositioned his vague experiment as the historically significant discovery of a "new man" - one "free from all fateful territorial ambitions and all aggressive or sadistic impulses".
The anthropologist decided that the "vast majority" of his guinea pigs found the experiment to be a success, and felt "more tolerant" than at the outset.
Reves did feel she had changed. "I had the feeling I could not continue my life exactly as before," she says.
However, a planned six-part interview in a prestigious Tel Aviv newspaper was stopped in its tracks by the outbreak of the Yom Kippur war. She resumed her medical duties, and moved to Munich with her naturopath boyfriend. Today she is happily married to another man.
In the decades following, Reves kept in touch with her Acali raftmates, using international conferences as opportunities to check in on her favourites, including Antoni and the Algerian-born Rachida Lierre, who was considered the sexiest woman aboard Acali.
Genovés went on to advise the UN on violence, and died in 2013.
I ask what Reves thinks of today's reality TV shows, which seem to be Genovés' most prominent legacy.
"It's certainly entertainment for the public. But it's not the real thing," she says.
Why's that, I ask. "On Acali, the main principle was that we could not leave. In all of this so-called reality, if you say 'let me out!' it's all over and you can just go home."
In retrospect, it's a miracle nobody went overboard.
