We live in a world in which the relationship between “nation” and “culture” matters. Central to that world are museums. They tell us important things about who we are, about national identity and identity politics.

The key lies in the relationship between roots and routes: where we have come from, who we are, and where we might be going.

Scotland is a nation in which these are very live issues. They also matter in the rest of the United Kingdom of Great Britain and Northern Ireland, to use its proper title. Where we have come from and where we might be going are live issues in these islands, and even in England, which contains 85% of the state population.

It is the rapid pace of social, cultural and economic change that makes people ask about their roots and routes. The debate in Scotland is especially lively. That is the lot of small nations inside big states. Look at the National Museum of Scotland to get a better sense of how we see ourselves and how others see us.

We used to have an argument (Scots are a disputatious lot), which went like this: our national culture was so distorted, unreal, and cringe-making –tartanry, brigadoonery, Harry Lauderism – that it prevented us seeing where our real political interests lay. Somehow we lacked the self-confidence to govern ourselves, and deferred to our English betters.

But hang on: don’t you Scots have a parliament now, and don’t most of you want even more powers, even independence? True, and some have argued that devolution is culture-lite, and much more to do with pragmatic policy improvements, and not about fulfilling some historic sense of national destiny and national cultural expression.

Bang goes another myth, for it turns out that Scots are well able to identify their national cultural symbols. It’s not all about politics, narrowly defined. So what matters to them as national symbols?

Our recent research in Scotland and England, asked people what are the symbols of being Scottish, being English and being British. It’s not the national flag nor even sporting achievements that matter most. It’s landscape, music and the arts – cultural matters, in other words.

And the English? For them it’s culture, too. Above all, it’s the language, English, which of course is no longer their exclusive property. The English and the Scots both value their own versions of treating people fairly – the English sense of fair play, and the Scots’ sense of equality; we’re a’ Jock Tamson’s bairns, as we say.

We know that only 4% of Scots and 16% of the English give priority to being British these days (which helps to explain why politicians bang on about making people feel British – they’re obviously worried).

Nevertheless, regardless of how they see themselves, people in both nations are quite happy to tell us what the symbols of British culture are: British democracy, the British sense of fair play, and even the monarchy as an institution (though Scots value that less than the English do).

The flag, anthem and sporting achievements matter far less, suggesting any impact on national pride due to the London 2012 Olympics will be shortlived.

So debates about national identity, about who we are and where we are going, are very much alive in these islands. At the heart of identity politics are debates about culture, and at the heart of those are museums.

These are the cultural spaces in which identities are contested, debated and fought over. And you probably have the scars and bruises to prove that.

David McCrone is emeritus professor of sociology at the University of Edinburgh. He is speaking at the Museums Association conference in Edinburgh