The venue was a former Victorian train depot on the north bank of the Liffey, beside Dublin Port. Built in the 1870s to house goods wagons, it had been converted to a live music venue called the Point Depot in 1988 and was already hosting big concerts when RTE booked it for Eurovision. Designer Paula Farrell built a stage four times the size of the one used in Millstreet the year before, with futuristic representations of Dublin skyscrapers, underfloor lighting representing the Liffey and Dublin Bay, and video screens embedded in the set. The theme was rivers. Cynthia Ni Mhurchu, fluent in English and Irish, and Gerry Ryan, the warm voice of RTE morning radio, presented in a mix of three languages. The capacity that night was around 3,200. The Point Theatre was demolished and rebuilt as the 3Arena in 2008. The river-mouth site, the water in front, the cargo ships docked nearby -- the location matters because Whelan's interval composition began with a slow string ascent meant to suggest exactly that: water rising and breaking.

The actual contest winner that night has been almost completely forgotten outside Ireland. It was a quiet ballad called Rock 'n' Roll Kids, written by Brendan Graham and performed by Paul Harrington and Charlie McGettigan, two middle-aged Irish singer-songwriters sitting on stools with an acoustic guitar and a piano. The song looked back at a 1960s rock-and-roll childhood with bittersweet warmth. It won handily -- 226 points, with eight maximum 12-point scores from voting juries across Europe, beating Poland (whose debut entrant Edyta Gorniak made history with second place) by 60 points. This was Ireland's sixth Eurovision win, more than any other country, and a record three wins in a row, never matched before. It also meant Ireland would have to host yet again in 1995, in Dublin once more. RTE's accountants reportedly considered burning the contest tapes.

Then came the voting break. As the juries telephoned their scores in, the screen cut to a wide shot of the stage and Bill Whelan's composition began. A slow Celtic vocal line from the choir Anuna built over rising strings. The RTE Concert Orchestra under Noel Kelehan kept the tempo gathering. And then two dancers walked on -- the Irish-American Jean Butler and the Chicago-born Michael Flatley -- and began a step routine that fused traditional Irish dance with something faster, harder, more flamboyant than anyone had ever seen on television. Behind them, twenty more dancers eventually joined in a line. The audience in the Point was on its feet within four minutes. By the seven-minute climax, the BBC commentator Terry Wogan -- a famously dry presence -- was shouting his commentary as if at a football match. The hall erupted. Across Europe, an estimated 300 million viewers had been brought to attention by what was supposed to be a filler segment. The single of the Riverdance theme, released a few weeks later, went straight to number one in the Irish charts and stayed there for 18 weeks. It is still the second-best-selling Irish single in history, behind only Elton John's tribute to Princess Diana.

Moya Doherty and her husband John McColgan immediately saw what they had. By February 1995 -- ten months after Eurovision -- they opened a full-length Riverdance stage show at the Point Theatre with Butler and Flatley again leading. Tickets sold out within three days. The five-week run extended; the show transferred to the Hammersmith Apollo in London; by March 1996 it had reached Radio City Music Hall in New York. It has since been seen live by an estimated 27.5 million people in 47 countries on six continents. Over 10 million home video copies have sold. Flatley left in 1995 after a contract dispute, formed his own show Lord of the Dance, and became a multi-millionaire. Butler stayed longer and is now a respected choreographer in her own right. Bill Whelan, who wrote the piece on commission for an Irish public broadcaster trying to fill seven minutes of dead air, won a Grammy in 1997 for the Best Musical Show Album. None of them have ever been hungry again.

There is a particular kind of magic in cultural moments that exceed their intended scale. The 1994 Eurovision interval was meant to be television wallpaper -- something for viewers to make tea over while the juries phoned in. Instead it set off a global reappraisal of what Irish performance could be. For decades, traditional Irish dance had been a careful, formal art: arms stiff at the sides, no expression on the face, judged by precise foot positioning. Flatley's contribution was to flagrantly violate that discipline -- chest out, arms swinging, grin enormous -- and Butler matched him with a softer, more athletic flow. The implicit claim was that Irish culture did not have to remain in the museum where the diaspora had carefully preserved it. It could be loud. It could be brash. It could be the headline act. Three years later, the Good Friday Agreement was signed and a new Ireland emerged. Riverdance was not the cause, but it was part of the soundtrack. The country had, at last, stopped apologising.