Measuring happiness is tricky; you may as well try to catch a butterfly with a hula-hoop.

Yet wellbeing is being mooted as a new currency to be assessed in international league tables alongside gross domestic product. According to Unicef, the Scandinavians have got things sussed when it comes to happiness. If they are in the premier league of parenting, then we are in division two. So I want to find out why the Danes and their children are so darned happy.

After a short flight across the North Sea and a swift train journey my nine-year-old son, Ruairidh, and I find ourselves in the middle of Copenhagen. There are bicycles everywhere. There are free city bikes for borrowing and sleeker models for hire. Our first lesson is that jay walkers take their lives in their hands. You have to look out for bicycles as much as you do for cars.

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We settle into our chic boutique hotel, the Square, and survey the city. Copenhagen has a pleasing skyline, largely comprised of solid stone buildings adorned with the occasional decorative dome or spire. It was constructed over centuries, utilising the proceeds from its position as a trading nation and even its modern buildings reflect a concern for quality and aesthetics. Such devotion to quality comes at a price. Denmark is not cheap but with judicious planning and by investing in a Copenhagen card, an enjoyable experience is within the scope of most budgets. The card costs around £50 for three days and entitles you to free transport. It also gets you into 60 attractions. (Children don't have to pay for transport and are free in many museums.)

We make the pilgrimage to Tivoli Gardens. Established in 1843, the pleasure garden is an elegant version of the theme parks which now proliferate. We enter a world of trees, flowers and illuminated water features with fair ground rides ranging from the old-fashioned merry-go-round to knuckle-biting opportunities.

There are plenty of happy kids but a lot of smiling adults too; some adults do not have children with them but they are laughing as they jump on and off rides. It is only day one and we feel we may have discovered two of the rules of happiness - cycle everywhere and maintain a life-long capacity to play.

On day two as we go to the National Museum, we see nine toddlers accompanied by four adults, two of whom are men. Each sports a luminous yellow vest so we deduce that this is a pre-school group. In Scotland those who fix cars get paid more than those who look after kids. Here in this crocodile of little ones a different picture is painted and it suggests that there is greater equality between men, women, and children.

At the museum, Ruairidh dresses up in Viking clothing and clambers into a long ship and fences with wooden swords. On Sunday we visit a science centre called the Experimentarium. Tickets for one adult and one child total £32 but the cost does not seem to impact on the venue's popularity. Perhaps high wages are another ingredient, although equality of wealth is probably key.

While Ruaridh explores, I look at parents. Mobile phones are nowhere to be seen. Everybody is too involved to bother with distracting personal gadgets. Adults and children enjoy each others' company. Child-care provision is high quality and highly subsidised, so most men and women work full time but family time is valued so the working day is short and free time is a time for togetherness.

So far so inspiring, but now it's time to check out how the Danes deal with rebels. We take a bus to Christiana, a former army barracks which was occupied by a group of homeless youths in 1971 as a commune.

We walk through a graffiti splattered alley and find ourselves breathing in pungent, herbal smoke. Cannabis is being sold and there are signs cursing the police.

This is all too much for Ruairidh. Nine-year-olds tend to be conservative, so we leave to find more conventional attractions.

Until now the authorities have put up with the hippies but its future may be in doubt as right-wing populists are on the march. What happens will be a test as to how progressive Danish society is.

I would like to revisit this city on my own. A less child-centred trip would free me to go back to Christiana to see if mainstream society is truly happy; happy enough to tolerate those who are not like them.

Getting there

SAS has return flights from Glasgow to Copenhagen from £180. Visit

Where to stay

Double rooms at the Square cost from around £98 per night including breakfast. Visit thesquare