You could tell it was getting serious when Gordon Brown made friends with Alistair Darling; and when the Scottish Daily Mail began running doom headlines about the future of the Union. I don't know whether the narrowing of the poll lead for the no campaign was just a blip, but it doesn't feel like it.

Something incredible is happening in Scotland. The little pin badges – Yes or No – that people wear are sparking open conversation: in the pub, the swimming baths, the post office queue. An entire country of 5 million people is asking itself, sometimes quite vociferously, what it wants to be.

It's even more incredible if you consider the possible outcome. If enough people tick the yes box, then come 2016 the flag of Great Britain will have to go minus a whole colour.

It probably won't happen. But few south of the border realise how volatile the outcome is. Yes, the polls reflect bookie William Hill's confidence that there's just a one in five chance of a majority for independence – but the variables are bigger than for most political events.

Having spent last week in Glasgow, I would say the biggest variable is going to be turnout. When political enthusiasm reaches the relatively apolitical world of the council estate, the pub, the nightclub and energises people, turnout can do weird things to poll predictions. Alex Salmond claimed there would be 80% turnout. I think the chances are even higher – and if the polls actually cope with such volume, every percentage point above normal introduces volatility not captured by normal polling.

At the Sub Club, a world-famous nightspot in Glasgow, the debate was remarkably coherent, even at 2am among the intoxicated smokers huddled outside. If I could distil the vox pops among those under-30s to a single thought it would be: "We want to run our own country."

They have heard all the dire macro-economic warnings – about the pound, the banks, the debt, the non-reliability of oil money. Set against the idea of making a clean break with Westminster politics and neoliberal economics, these are risks many of them are prepared to take.

One reason the political class is not hearing the debate properly is that, on each side, there are mismatched political leaderships and tin-eared campaign groups. On the yes side, many of the young people I spoke to despise Alex Salmond. On the no side, it's fair to say Alistair Darling is not hugely representative of a coalition that includes people from the Orange lodges and the Scottish Tories, and the gay clubbers I met who were firm no voters.

If, on the morning of 19 September, we wake up and that 4/1 horse of independence has come in, the levels of shock in official circles will be extreme. The Conservatives will have presided over the breakup of the Union. Even compared with handing Zimbabwe to Zanu-PF, and Hong Kong to the Chinese Communist party, that will be a major psychological moment.

Even more traumatised will be Labour. The prospect of a majority Labour government at Westminster after 2016 will be remote. The party in Scotland will likely go into meltdown, with a Podemos-style left emerging among the pro-independence Labour camp, the Greens and the progressives around groups like Common Weal.

There will be immediate ramifications beyond the UK: in Madrid and Brussels there will be outcry; in Barcelona public joy; in Moscow quiet glee.

But the official narrative does not allow us to consider the possibility of a yes victory. The political class – and I include Salmond's SNP in this – is like the tightroper wobbling on a wire between two skyscrapers. Its members can't allow themselves to think of the consequence of falling off. The old certainties will be so dead anyway that it will scarcely matter.

What we can say, already, is that the no campaign – for all its resilience in the opinion polls – failed in its plan to turn the referendum into an issue of macro-economic risk. If it has worked, it is among the older population and not the majority of the young.

The most coherent of the young people I spoke to understood the macro-economic risk. But they weighed it against two increasingly intolerable burdens: the inability of Scotland's relatively left-leaning electorate to influence Westminster; and the inability to budge Scottish Labour away from the free-market and pro-austerity policies associated with Brown and Darling.

What this means is, even if the yes vote fails on 18 September, scoring somewhere in the mid 40s, the pattern of all future Scottish independence debates is set.

Independence has become a narrative of the people against big government; about an energised Scottish street, bar and nightclub versus the sleazy elite of official politics.

Alistair Darling, leader of the Better Together campaign. Photograph: Andrew Milligan/PA

And in response, the left part of the pro-union camp has had to develop its own, "more radical than Darling" rationales. It's not something you hear from the Westminster parties, but via social media I have picked up a strong meme among Scottish trade union members that independence under the SNP is "not radical enough to bother".

Once established, political psychologies like this do not go away. History shows they intensify until something gives, and at some point it is usually the borders of a nation state.

What we know already is that a significant number of Scottish people have a dream: where statehood, social justice and cultural self-confidence fit together into a clear and popular project.

The rest of Britain may be stunned, but should not be surprised if the enthusiasm for this dream propels enough people into the voting booths to give the yes camp a narrow victory.

If it happens there'll be a lot of finger pointing, but it's obvious in advance where the biggest problem lies: it's become impossible to express opposition to free market economics via the main Westminster parties.

Some English and Welsh voters think they're doing it by voting Ukip. But the referendum offered Scottish voters a way to do it by destroying the union. Whether you think that's illusory or mistaken, it's formed the narrative on the streets.

That's where we should be watching now; the high-camp shouting match of men in suits is a diversion.

Paul Mason is economics editor at Channel 4 News. Follow him @paulmasonnews