The stadium holds 80,000 people, and is always full to bursting for American football matches. But there are only 11,000 students at the University of Notre Dame. To understand the discrepancy, you have to go to a game on a day like today. Autumn light streaks off the huge glass pod that houses the media and sweeps the crowd with glare and shadow. The visitors' brass band marches in, more than 100 instruments strong, in comic-opera uniforms: bouncing black plumes, cream plastrons. The drum major is lithe and leaping, using his baton as a bar for a stunning limbo dance. The visitors' acrobats caper behind him. Their women are spectacular - frankly erotic in spangly leotards and shiny blue matador capes.
After a few minutes' dizzying entertainment from the visitors, Notre Dame's band arrives, three times the size of its rival, with snaking tubas gleaming in the sunshine. You immediately feel the moral superiority. Our cheerleaders are charming but demure. No cavorting acrobats lead the way, but the solemn, stately Irish Guard - a corps of uniformly tall undergraduates in ostentatiously big bearskins and bright plaid, whose name, like all Notre Dame's football nomenclature, proclaims the Irish preponderance in the university in the 19th and early 20th centuries. The team is the "Fighting Irish". "We are Irish," the students and faculty proclaim, rising blithely above their own diversity of colour and culture.
The band dances its way through jazz adaptations and march themes, culminating in the Notre Dame victory march. "Cheer for old Notre Dame," sings the crowd. "Shake the thunder from the skies." Europeans experiencing US college football for the first time are already baffled by the outrageous scale of the brouhaha. But for the home crowd, it's routine, as is the strange, patriotic ritual that follows. Everyone stands. Highlights from the Declaration of Independence and the Constitution of the United States resound over the PA system. The Irish Guard raises high the Stars and Stripes as the national anthem echoes. For a moment - just before the climactic invocation of "The land of the free and the home of the brave" - the music hangs in the air. A mechanical roar deafens the stadium. Eyes turn heavenward. A flight of the US Air Force screams through the sky in salute.
American football at Notre Dame can never be "only a game", because for generations Catholics in the US had to struggle against prejudice and suspicion. Past generations of Notre Dame footballers were literally "fighting" Irish, challenging the Ku Klux Klan in the streets. By beating white Anglo-Saxon Protestants at their own game, Notre Dame achieved a unique status in US life as a university with a national following, embracing a community incomparably vaster than that of its own alumni.
Even a phlegmatic foreigner like me finds the excitement irresistible as the game begins. The rules are as hard to understand as the pre-match rites. At Notre Dame, every game is on national network television; so the programme allows plenty of airtime for the advertisers, as well as for the constant shifting and shunting of players. The performance is studded with acrobatic interludes, the bands' bravura, and emotional appearances by Notre Dame heroes. Surviving members of a record-breaking football squad of the 1930s parade. So does the current women's soccer team ("ranked fifth in the nation", the PA tells us). So do students who have tended to victims of the Haitian earthquake.
The interruptions make every interval of play intense. With a narrow lead, we lose the ball in the closing moments. The visitors look menacing. Somehow our defence holds out for the win. The stadium erupts in joy. It's curiously uniform, predictable joy, adjusted to the rhythm of the band and the dictates of tradition, as the crowd rises in unison to sing the school song and pound the air together at the closing line, "Our hearts forever love thee, Notre Dame."
The balletically disciplined manoeuvres of the team on the field, the clockwork of the crowd, the regulated display of acrobats and bands, the proclamations of patriotic commitment - everything proclaims an unknown truth about American greatness. Life in the "land of the free" is surprisingly self-regimented. This is a culture of conformity, solidarity and intense communal awareness. The spirit of America is collaborative, not rabidly individualistic - forged in wagon trains and small towns, not mavericks' corrals and lone ranges.
I head out of the stadium, pausing to watch the visitors' band march past, tight-lipped and sad-eyed as they drum a dirge. The crowd turns, streaming towards the campus basilica, as the chimes cascade. I realise a deeper truth about football at Notre Dame - for some, perhaps, harder to understand even than the rules and the razzmatazz. For, win or lose, those bells always ring out for mass when the game is over, with the same mingled notes of triumph and sorrow, summoning us to another kind of sacrifice. The victory that counts is not of this world, and has still to be fought for.