IT looked like a good day out, if you like that sort of thing. Thousands of people marching through Glasgow in support of Scottish independence; hundreds of placards and banners; a constant soundtrack of drums, whistles and bagpipes, and even a few dogs decked out – presumably with their permission – in Yes2 stickers. And flags of course. Flags upon flags upon flags.

For those on the ground in Glasgow, there was no doubt about the message the march was sending out. “Apparently there’s no appetite for independence but look at this!” said one. “Tens of thousands are marching for independence,” said another, “it will come soon.” In other words, the further they walked, the more the marchers felt what they’d always known – that the polls, and the psephologists, and the media are wrong, that independence is inevitable and it will happen to the sound of marching.

However - exciting though the weekend’s festivities were - it seems to me that the marchers have got it pretty badly wrong. In fact, by my reckoning, they have made at least four miscalculations in thinking that an event like this will serve their cause. They say they will keep on marching until they get their way, but could they end up heading in the wrong direction?

The first mistake is one that, to be fair, we’re all guilty of sometimes, which is to assume that because the people around us think one thing, everyone does. There you are, surrounded by people telling you independence is inevitable, so you make the mistake of overestimating the extent to which your views are shared by others. It happens on social media all the time, but it can happen on the street too: you create a consensus that’s in your head; a false consensus.

The evidence for the false consensus at the march can be seen most obviously in the polls, which show support for independence steady at 45 per cent, but it can also be seen in the marchers’ attitude to the media. One of them complained about The Sunday Herald using a picture of counter protesters waving union flags, the suggestion being that the picture was a distortion of what really happened. But this is about a picture of reality not fitting with the picture in someone’s head; it clashed with the false consensus.

The second mistake is to assume that the march will increase public support for independence. The event was organised by a coalition called All Under One Banner, but the problem with a broad church is some of the people who end up worshipping there. The loudest speaker on the day was the former Scottish Socialist leader Tommy Sheridan, but is he really the kind of person to broaden the appeal of independence? He also told the crowd not to be “swayed by the Unionist narrative that tells you that we don’t have the majority.” In other words, false consensus writ large.

There are other issues with the idea of the march as a way of increasing support for independence. For a start, it has highlighted divisions, with many of the marchers emphasising that the event was “grassroots-led” – code for nothing to do with the SNP leadership. Some observers may also have a problem with the ramshackle iconography of the march itself – aggressive banners with phrases like “Smash the Union” for instance. And there will always be some, especially those with a good knowledge of the history of nationalism, for whom a sea of flags is a turn-off and a threat.

Which takes us to the third mistake: the belief that the Scottish Government should go for a quick referendum to take advantage of Brexit. The theory among the marchers goes like this: 2014 was an uphill battle because the choice was between so-called stability in the UK and the unknown. But this time, it’s different, and better: the choice would be between independence and Brexit Britain – in other words, the unknown versus the unknown and that would increase the chances of a Yes vote.

However – despite the impatience of the marchers – the theory doesn’t stack up, mainly because it misunderstands how many No voters, and some Yes voters, think. Independence may feel inevitable to the marchers, but many No voters think that in the uncertain world of Brexit, independence would simply pile on more uncertainty. And using Brexit as an argument for independence is also tricky for Yes voters who voted to leave the EU. The SNP needs the 45 per cent from 2014 to stay solid, but if you started to lose some of them over Brexit, you would need even more Unionists to switch from the other side and that looks like a tall order.

An early vote on independence comes with other problems too. For example, would the SNP really have time to get their facts sorted – on the economy for instance, and the currency? Trying to get those arguments in place looks daunting, whatever the marchers think.

So what about their fourth mistake? Many of the marchers – Tommy Sheridan among them – said it was vital to hold another independence referendum before the next Scottish general election when the mandate could run out. “We fought long and hard for it,” bellowed Mr Sheridan, “and we should use it.”

But again the enthusiasm and passion hides an error of strategy and fact. Remember that agreement signed by David Cameron in 2012 to permit a Scottish referendum? Can you imagine a Conservative Government in the middle of Brexit and supported by the Democratic Unionists doing the same thing? It isn’t going to happen, which means that rather than marching for a referendum now, the only option is to plan for a legal referendum in the longer term.

Whether Nicola Sturgeon will do this is another matter. The First Minister will have been watching the march at the weekend and will know what it represents: a desire to get going and do what the marchers see as inevitable. But she’ll also be listening to voices in her party, including her own former advisor Noel Dolan, that the focus should be on Brexit not independence. Who Ms Sturgeon listens to is up to her, but if the Glasgow march has proved anything, it’s that listening to the man in the street is not always the wisest option.