A protest in Puerta del Sol square in Madrid, what could be more appropriate? After all, one of Spain's most iconic images is Goya's depiction of a riot there, The Second of May. There you can see a bunch of Spaniards taking on Napoleon's invading army. And it was also in Puerta del Sol that a crowd succeeded in ousting the king in 1931 and proclaiming a republic. Since then the square has lost almost all of its rebellious soul, having been transformed into a tourist spot. It has gone from a place of memory to a place of souvenirs.

That is, until Sunday when a rather obscure demonstration turned into a permanent rally, which is gaining momentum by the day and has gathered thousands already.

Tellingly, they're being described not in political but emotional terms. They're the indignados, "the angry ones". Angry at the banks, at the labour market, at the main political parties and most of all at the politicians, who they feel don't represent them. What they actually want is less clear. They pride themselves on not having leaders or a specific political platform, an ideological fuzziness that has enabled them to attract a diverse constituency.

They have taken the politicians off guard, that's for sure. Both the ruling Socialists and the conservative opposition, the People's party, are in shock. Not at being criticised but at being bundled together as "the same thing". In next year's general election the socialists were counting on the fear the conservatives instil in many Spaniards. The conservatives were counting on the anger aroused by the socialist government, among many others. Now that anger seems to be directed at both parties and it is both that are afraid. "Against the big parties" is one of the main slogans. And there's another election (local and regional) even closer, on Sunday.

The media seems puzzled, too. Abroad it is portrayed – mistakenly – as a protest against the government's austerity measures, approved a year ago. In Spain, newspapers are also awash with analysis trying to understand the supposedly complex nature of a political movement that is seen as something radically new. At times it's characterised as "post-democratic" or "trans-ideological", a "new way of understanding politics" or even a "rejection of politics". The unsurprising fact that many of those taking part possess mobile phones and computers also allows for the now mandatory amazement at the power of the internet. So is it ideology or technology?

Well, the reality may be less complicated.

The first demonstration was organised through the internet, but it gathered a modest crowd. It was only when the police forcibly removed the demonstrators, and the news was broadcasted by TV, that most people learned of the protest and its numbers began to grow.

The makeup of the protestors is not that mysterious if you take a walk in the square. Those who camp there are unmistakeably part of the anti-globalisation camp, focused in social causes (immigrants' rights, world hunger), idealistic, often naive, and with a strong anti-capitalist bent. They're actually very few.

What is new here is that at times they're reinforced by a much wider and down-to-earth crowd. It's comprised of pensioners, passersby and angry parents, but still mostly of university students. The People's party knows these are not their potential voters. If they're angry at the Socialists it is because they feel it has shifted to the right in the economy, which is true. The hardcore may be "post-democratic", but the ensemble is certainly not "trans-ideological".

I believe this is the key to understanding this protest. For all its far-reaching rhetoric, it addresses solely the left. It ultimately represents the frustration of those who see that it doesn't matter which way you vote, the economic policies are dictated by the markets; hence the critique of "the system" and the demands of accountability and transparency. Most of the protesters seem to be the people who voted Socialist in 2008 only to prevent a win for the People's party. They don't want their vote to be taken for granted yet again.

Will they succeed? The difficulties facing a movement of this sort are daunting. First they will have to withstand the disappointment of an almost certain People's party victory in Sunday's election. If they survive that, the Socialists, who are in the process of changing their leadership, will try to co-opt at least part of them with new promises – likely to turn into new disappointments. Those remaining may try to form a party, but then they will have to have leaders and a platform, it will be just like any other party.

They better enjoy their present success. They may not change Spanish politics forever, but they have succeeded in something difficult enough: in putting all politicians to shame at least for a few days.