The big bronze bull is surrounded by metal fences and strategically placed members of NYPD's finest. The famous statue, the symbol of aggressive market optimism, is normally open for tourists to grope and fondle, but today, in part because of the "Occupy Wall Street" protest, it has been penned. Today, the Wall Street Bull looks amusingly like a panicked animal in a cage.

It might have been spooked by the couple of thousand activists, hippies, union members, laid-off workers and schoolkids camped out around the corner in Liberty Plaza. When I arrive at Occupy Wall Street, they've already been there for a fortnight, and have turned the square, which is normally scattered with City workers snatching lunch and chattering on their smartphones, into a little peace village, complete with a well-stocked library, free kitchen, professional childcare centre, sleeping areas, meeting spaces, and crowds of young people dancing and playing music.

The protest, which began on 17 September after a call-out by activist magazine Adbusters and the hacker collective Anonymous, has swelled from its original few hundred members after a weekend of police crackdowns. Images of New York police pepper-spraying young women in the face and arresting peaceful protesters spread around the world, which has been shocked not so much by the response of the police in a city where the term 'police brutality' was coined, but by the fact that here, in America, at the symbolic heart of global capitalism, ordinary people have turned off their televisions and come out to shout in the streets. "I never thought I'd live to see this in New York City," says my friend, a native New Yorker, as we watch a drum circle forming underneath the looming skyscrapers of Manhattan's financial district, speckled with rain.

Right now, as I write from the occupied Plaza, a mass arrest is taking place on Brooklyn Bridge, where 2,500 activists have marched to express their distaste for corporate greed. 'Banks got bailed out - we got sold out!' chanted the marchers, hesitantly at first, and then more confidently, keeping to the sidewalks, before they were led onto the car portion of the bridge by police - who promptly sealed the exits and began to arrest everybody.

The entrance to the Bridge is now completely sealed by a quadruple line of cops, as reports come in that a journalist from the New York Times has been arrested. Marchers on the other side yell angrily at the police to let their friends go. "Come join us!" they shout. "You are the ninety-nine percent!"

They mean that the police, like the protesters, are part of the "99 per cent' of the population whose livelihoods are threatened by the financial crisis, as opposed to the 1% of wealthy Americans still raking in profit. "We are the 99 percent," says the group on its Tumblr site. "We are getting kicked out of our homes. We are forced to choose between groceries and rent. We are denied quality medical care. We are suffering from environmental pollution. We are working long hours for little pay and no rights, if we are working at all. We are getting nothing while the other 1 percent is getting everything. We are the 99 percent." It's a very polite way of saying 'class war.'

The '99 percent' statistic has become emblematic of the American wing of what is phrasing itself as a global protest movement, taking its inspiration from square occupations in Egypt, Greece, Spain and Great Britain. Another statistic you can see daubed on placards around the Plaza is that the wealthiest 400 Americans have more combined wealth than the poorest 150 million. Later in the day, the United Steelworkers union becomes the latest in a growing list of labour organisations and non-profit groups to throw its support behind Occupy Wall Street, ahead of a united march next Wednesday.

Economic inequality is a consistent undertone, but at times this occupation has the feel of a music festival; drifting through the square are young people who seem to have walked out of a wormhole from Woodstock, including a boy with dreads and tiedye scarves sitting on a skateboard next to a sign asking for 'donations for adopting puppies.'

I ask him what the puppies are for. 'Emotional support,' he tells me. Elsewhere, a young woman with long hair is handing out posies. "You're very beautiful," she says, smiling, "have a bottle of flowers." All of these people appear to be disturbingly sober: nobody wants to give the NYPD an excuse to crack down.

Not that they need an excuse. There can be no swifter political lesson than the first blast of pepper spray to the face received by a middle-class protester, and right now a lot of American activists are learning fast. "No Bulls, No Bears, just Pigs," reads one sign. As the light fades and the rain starts to come down hard, hundreds of protesters, reporters and members of the press are still trapped on the bridge. In the pouring drizzle, they strap their backpacks onto their fronts so the police can't take them, according to Kristen Gwynne, a New York writer. Gwynne tells Alternet that protesters are singing to keep morale up: 'this little light of mine.' Hundreds more are cuffed and on vans headed to jail. "I had a feeling as soon as we walked onto the bridge that this wasn't going to end well," says Michael, a member of the march. "The police allowed people to go on the car ramp on the bridge, and when they realised what was happening, people started jumping onto the pedestrian side, but then it was too late." Young teenagers are among the arrestees, in scenes extremely reminiscent of the Westminster Bridge kettle in London in December 2010. "You can't arrest an idea!" the protesters yell.

But what is the idea? The most consistent criticism laid against the occupiers is their lack of a central organising system or core message. Who are these people, and what do they want? The fact that the mainstream media is even asking this question can be considered a victory for the Occupy Wall Street.

Part of the point of this occupation, like the occupations in Greece, Spain and London, has been to create a different kind of political space, a temporary reality outside the lassitudes of mainstream politics where human beings are equal and respected. People have come from all over the country and all over the world to be here, and not all of them, contrary to most of the reports, are white and college-educated. I meet black high-schoolers from Brooklyn, young men from California, young women from St Louis, Maine and Wisconsin, older laid-off workers from Texas and Virginia, and activists from Spain who have come to see if America can really host the kind of revolutionary space that has been opening up across Europe and the Middle East. It seems that, in its own way, it can: copycat protests are opening up across the country, from Chicago to Denver to Los Angeles and Boston.

As night falls in New York, in a bright, busy space under some colourful tarpaulins, the media team is working flat out to deal with international press enquiries, as reports come in that 700 protesters have been arrested by the New York Police Department (NYPD). There is a tense, frenzied atmosphere, with laptops flung down in between knots of cables as volunteers scarf down donated pizza and field information coming in over the wires. Outside the media tent, thousands of people are taking part in a mass meeting, huddled inside plastic ponchos and under umbrellas. NYPD have forbidden amplification, so anything said at the front is immediately chanted back by three hundred voices so that the rest can hear, giving the meeting the call-and-response a feel of a sermon. Every evening, these large General Assemblies gather to debate the demands and direction of the group, and a loose statement is eventually agreed by consensus and published in the group's newspaper, the "Occupied Wall Street Journal."

So far, it's pick-your-own cause, with grievances ranging from bank bail-outs to animal testing, and yet what most of the mainstream media seems to have missed is the fact that the occupation itself is its own demand. It's a symbolic and practical reappropriation of space at the heart of the world's most financially powerful square mile, an alternative community opening up like a magic window on a fairer future.

Activists wandering back from the bridge are greeted by strangers with open arms, as members of the 'comfort' team dash around taking care of everyone. There is free coffee, free food, a young lady with a lip-ring offering free hugs, and painted signs saying "Freedom". Nobody expected the occupation at Liberty Plaza to last this long or to become this important, but the mass arrests today have ignited public anger and drawn the attention of the press across the world. Whatever happens next, Occupy Wall Street is sending a message to the American people: the 99 percent are still here, in the shadow of the glittering palaces of global finance, and they are beginning to dream dangerously, and they will not go away quietly.