It’s a hot, humid evening and I’m sitting on the ground with around 50,000 other people, all about to watch Cloud Gate Dance Theatre give its annual outdoor performance in Taipei. The atmosphere in Liberty Plaza is extraordinary. I can’t think of another dance company in the world that could draw so large and so festive a crowd. Most of the audience have brought picnics, many enduring a day of rainstorms to bag a position close to the stage. Yet, although this is a special performance – one of the last before Cloud Gate’s founding director Lin Hwai-min steps down – such devotion has been normal for the company almost since it was formed.

Cloud Gate was named as the outstanding company at the British National Dance awards last year and is a headline attraction of the new Sadler’s Wells season. Lin’s success in turning a small experimental dance company into a national icon and international brand is a remarkable story. Now 71, with a fierce energy and a huge crinkled smile, Lin acknowledges that he had almost no experience of professional dance when he staged his first programme back in 1973, and discovered that he’d sold 3,000 tickets for just two shows. “I almost had a nervous breakdown,” he says. “I thought, ‘My god, now I have to learn how to choreograph.’”

I am from a generation who believe it is their duty to make a difference Lin Hwai-min

In the south of Taiwan, where Lin grew up, there had been very little dance to see. At the age of five he fell in love with the film The Red Shoes but nine years later, when he took his first ballet class, it proved a huge disappointment: “I had a book, All You Need to Know About Ballet, and I could tell that the teacher wasn’t doing things correctly.” Already a precociously literary teenager, inspired by Hemingway, Fitzgerald and classical Chinese poetry, Lin focused his energies on becoming a writer. By the age of 22, he’d published his first collection of short stories and had been offered a fellowship at the International Writers’ Programme in Idaho.

Once he arrived in the US, though, contemporary dance grabbed his imagination. Lin was able to see the companies of Paul Taylor, Merce Cunningham and José Limón – and take classes at the Martha Graham school. He even created his first work: a tortuously complicated piece, he now realises, about “a philosopher who dreams he becomes a butterfly”. When he returned to Taipei, he was by default the local expert on contemporary dance. With musicians, dancers and artists all curious to know more, he was persuaded to set up a company.

Facebook Twitter Pinterest Beckoning by Cloud Gate 2, a sister company set up to enact grassroots change. Photograph: Tristram Kenton/The Guardian

“I was stupid,” he says. “I was very young but I came from a generation who believed it was their duty to make a difference to the world.” The works Lin began to choreograph blended modern dance, classical ballet, Chinese folk dance and Chinese opera, grounded in the silken stillness of tai chi. They also drew on distinctively Taiwanese subject matter: Portrait of the Families addressed the massacre of political and intellectual dissidents under Chiang Kai-shek; the pastoral masterpiece Rice evoked the rhythms and landscape of rural Taiwan.

This choice of local subject matter was radical in itself: during the 28 years of Chiang’s regime, as well the Japanese rule that preceded it, the island’s language and culture had been brutally repressed. When Lin created his 1978 work Legacy, about early Taiwanese settlers, he had to stage the premiere in the south of the island, far away from the National Security Bureau in Taipei.

Facebook Twitter Pinterest Mentor … Lin Hwai-min, left, with Cheng Tsung-lung. Photograph: Liu Chen-hsiang

But as challenging as those early years were, Lin says: “It is wonderful to be an artist here. In 1987, we ended martial law. In 1996, we had our first direct presidential election. Now we have a woman president and we have legalised gay marriage.” It matters profoundly to him that he has been an instrument for change, helping to found a flourishing dance department at the National Arts University and using a second company, Cloud Gate 2, to bring dance classes and performance to impoverished regions of Taiwan.

The love he’s earned is palpable. Back in the early 90s, when he tried to shuck off the exhausting burden of Cloud Gate, Lin was shamed into returning by a reproachful taxi driver, who said to him: “There is hardship in every profession, Mr Lin. It is hard for me to earn a living in the traffic of Taipei. But we need Cloud Gate. So drive on.”

In 2008, when the company’s rehearsal base was destroyed by a fire, Lin did not have to ask for help in building a new home: more than 4,000 people spontaneously sent donations, including one small boy who offered all of his pocket money. While others might cling on to such love, Lin is adamant that he’s “simply looking after a public property”: his final gift to Cloud Gate will be to step down at the end of this year having created as smooth a transition as possible for his successor.

Lin has been mentoring Cheng Tsung-lung for years, watching him develop as a dancer and choreographer, appointing him director of Cloud Gate 2 in 2014, but he’s delighted that Cheng is a very different artist from him. “I came from a family of poets and scholars but Tsung-lung came from mud,” he says. “I envy him that.” Lin points to that fact that, while his mother made him listen to Schubert and Beethoven after school, Cheng’s parents had him working the street markets from the age of eight, selling slippers made at his father’s factory.

The two men do, however, share a childhood interest in dance. Cheng, talking through a translator, says he was “a very active little boy, always bumping into things, with too much energy” and was sent to dance classes to calm down. He describes how rapidly he learned that showing off his moves in the market brought business to his stall. Even though he endured a troubled adolescence, getting involved with serious drugs and sentenced to two years’ probation and community service, Cheng continued to stick with dance.

When there was a choice between going into the slipper factory or going to university, he opted to study dance at degree level. “It was the only thing I was good at,” he laughs, although he says it was only when a back injury forced him to focus temporarily on choreography that he discovered a true sense of vocation. “When I was a child, I used to make up stories about the people on the street. I didn’t have many opportunities to go to cinema, and it was like making my own films.” Once Cheng realised that creating dance was like an extension of those childhood fantasies, his work developed rapidly.

Facebook Twitter Pinterest Against the grain … a performance of Song of the Wanderers by Cloud Gate. Photograph: Yu Hui-hung

Lin says it’s been one of the highlights of his career to watch Cheng mature: “He gets scared, turns into a skeleton during the creative process, but it is wonderful to see. His work is very different from mine, very dark, and he can speak to the internet generation in a way that I can’t.”

13 Tongues, which Cloud Gate will bring to London next year, is typical of Cheng’s work in its fusion of local Taiwanese culture, contemporary music and a sophisticated digital sensibility. It’s a fantastical but deeply urban piece, redolent both of ancient superstitions and the clamour of modern Taipei, with black-clad dancers massing in ritualised patterns against a digitally created art work, calling out the raucous rhythmic chants of street hawkers and singing Taoist chants.

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Cheng, aged 43, talks and dresses like a member of modern, edgy Taipei, but he brings a very old-fashioned sense of commitment to his job: “My responsibility is about how I can keep on working for dance and connecting it with all the people here,” he says, recalling his first experiences of community work with Cloud Gate 2. “We were going into remote parts of Taiwan to help people liberate what’s inside of them, and it reminded me of when I was a child, when the street vendors would start playing their cassettes and everyone would be dancing and enjoying their bodies.”

His reverence for Cloud Gate’s contribution to the island as a whole is touchingly direct. “It has brought us inspiration and dignity. At first, when people came to watch the company, they didn’t know how to behave in a public place, they didn’t know about not talking or not leaving their trash. This society loves Cloud Gate and Mr Lin – but Mr Lin has also brought society to a higher place.”