Throughout 2012 and the first part of 2013, a comfy misapprehension seemed to have settled among those whose job is to analyse world events: that, aside from continuing turbulence in the Arab world, the huge surge of protest that defined 2011 had long since died. This plotline was never entirely convincing. It is less than a fortnight since there was a general strike in Greece, such blighted eurozone countries as Spain and Italy have hardly been models of quiet and obedience, and protest movements in such wildly diverse countries as Chile and Israel have not gone away. But in the UK and US, the demise of Occupy fed into a banal but effective story: that camping in city squares and decrying the general state of things is so 2011, darling.

But now look, chiefly at Brazil, where protests have rippled through around 80 cities, with clear echoes of events two years ago. Inevitably, everything is organised via social media; as happened in 2011, exactly what anyone wants seems less important than the general outlines of dissent, and the simple experience of being involved. There has been surprise that such convulsive events have happened in a country seemingly transformed by the ruling Workers' party, where unemployment is at an all-time low. But therein lies proof that deeper factors are at work, and the country seems to be sounding a great popular wail about a distant state and cronyish elite. "This must be a nation where people have a voice, [and] we don't have a voice any more," runs a typical statement from a protester. To quote from a Financial Times report: "While much has changed in Brazil, the protests highlight those things that have not – repressive and outdated policing, an inefficient state, and an often corrupt and ineffective political class."

The protests in Turkey seem to be brimming with similar stuff, as Prime Minister Recep Tayyip Erdoğan apparently acknowledged towards the end of last week. "The same plot is being laid in Brazil," he told a crowd of supporters. "The symbols, the banners, Twitter and the international media are the same." He was trying to pin the blame on an outside conspiracy, but in a different way, his words rang true.

Fundamentally, what has been popping up around the planet for over two years is not about austerity, or the rest of the fallout from the crash of 2008, as important as they remain. Its central tension is surely between a revolution in communication that is transforming people's expectation of influence and voice, and closed networks of power that tie together corporations and government. If you haven't already read Paul Mason's brilliant book Why It's Still Kicking Off Everywhere, I'd suggest you do so – and begin with a quote halfway through, from the internet theorist Clay Shirky: "Most of the barriers to group action have collapsed, and without those barriers we are free to explore new ways of gathering together and getting things done."

To millions of people, life can now be open, endlessly expressive, and full of collaborative groupings that come and go – to use a word beloved of people who write about these things, horizontal. Power, by contrast, is ever more vertical, sealed off from daily life, and guarded by hardened cliques. And yes, there is a glorious contradiction in the fact that the internet giants responsible for all this are, on close inspection, securely built into the same structures that people are now taking against. Then again, capitalism, as two Germans once came to tell us, is full of contradictions; that's half the fun of it.

Brazil is a particularly fascinating case study, because it shines light on how awkwardly this new reality sits with even the most forward-looking parts of the mainstream left. Orthodox social democracy would have you believe that the essential relations between citizen and state can remain largely unchanged, so long as money goes from rich to poor, and society is understood to be on roughly the correct path. But the politics that has flashed to life around the world since 2011 proves that this is increasingly insufficient. The state is a massive part of the problem – whether that is somewhat masked by progressive intentions, as in Brazil; or stark-staringly obvious, as in countries where cuts are in full effect, and government is currently sloughing off its residual social-democratic obligations.

This is why, irrespective of election results, there will be many more flashpoints around the planet, and politics – here as elsewhere – will sooner or later have to be reinvented. On the left, most people remain in thrall to a worldview little changed since the early 20th century, whereby the top-down state can supposedly be captured, and used to tame an inhuman market. But what does the state do now, as a matter of in-built logic? In Britain, it props up banks, humiliates the poor – and, as we know now, scans everybody's emails and mobile phone records. Even when it is seeing to its more benign functions, it is now so cold and target-driven that initiative, empathy and care are often nowhere to be seen.

"I'd have to say there is far too much bullying and harassment, nepotism and patronage," says one former hospital boss about the NHS; he may just as well have been talking about any part of the machinery of politics and government. So it is that you arrive at what might tie together South America, and our small corner of northern Europe: sitting on top of a tangle of problems, that self-same inefficient state, and ineffective political class. The latter, moreover, are now the same tribe, across the world: they wear Joe 90-style glasses and nondescript suits, attend international summits on "governance", and so fumble with social media that their unease with the new reality is obvious.

It is in the nature of protests that people are impatient for change. But all this is so huge that it will take decades to work itself out. Across the world, parties of both left and right will either be transformed or disappear; in more and more countries, protests will flare into life, and then go quiet. Ugly populism and the hard right could very well prosper; social democracy may spend a long time in retreat. For good or ill, it's going to be a very interesting century.