Running alongside the contrived culture of Edinburgh in August is Just Festival. To quote directly from its programme of events: "Just Festival celebrates that peace is not only an absence of conflict; it is a presence." And so I was privileged to participate in an event last Monday evening called Syrian Without Syria, organised by a magnificent organisation called Mercy Corps, which is currently engaged in relief work among refugees in Syria.

Like many others, my knowledge of what has been happening in Syria has been gleaned simply from being moderately aware of events there following the initial euphoria of the Arab spring three years ago. My attitude was probably one of mild concern built on a complacent and haphazard western instinct.

It could be characterised thus: this is a volatile region where conflicts seemingly run endlessly into each other and arise from each other's ashes. There will be a television advert along in a minute where I can donate some cash by pressing some buttons – and then it's back to the Champions League.

The numbers coming out of Syria, though, are devastating. Quite simply, one of the world's oldest and most noble civilisations is being destroyed before our eyes. More than 160,000 people have already been killed, at least half of them civilians. Nearly 10 million people have been driven from their homes. Around half of the country's prewar population now requires humanitarian aid.

By the end of 2014, the UN estimates that more than 4 million people will have sought refuge in neighbouring Iraq, Jordan, Lebanon and Turkey, countries whose political and social infrastructures are not ideal for coping with such sudden movements of peoples, but whose wells of generosity and compassion are constantly being visited, something we ought never to forget when next we are coaxed into lazy assumptions about these societies.

Why should we care more than usual about Syria as Gaza burns, Ukraine shakes and genocide stalks a mountainside in northern Iraq? Aren't there limits to our capacity for compassion? The sheer numbers in Syria, though, and the size of this wave of human suffering, must surely call forth from us a more considered and thoughtful response.

In multicultural Britain, we can no longer afford simply to wash our hands of this. Our children and their children are taking partners from across ethnic, cultural and religious boundaries. Many more of us are liable to be touched by a humanitarian crisis of this magnitude, no matter how indirectly and no matter how many times removed. In similar circumstances and left to fall on the mercy of affluent and unaffected countries, we would all hope for a compassionate and kindly response. However, the world's asylum seekers and refugees are getting very little from any of us in Scotland, Glasgow apart.

For 12 days in July and August, our neighbours in the rest of the United Kingdom and in the Commonwealth beyond got a glimpse of just how big a heart my city possesses. At the Glasgow Games opening ceremony, Billy Connolly told us how Glasgow was the first city in the world to stand beside Nelson Mandela in his cell on Robben Island. And for more than 15 years the city has become one of the main destinations for refugees and asylum seekers pitching up on Britain's shores.

Outside of London, it is the largest dispersal area, taking around 10% of asylum seekers who come to the UK. In a deal struck with the UK government, Glasgow has been opening its doors to thousands of families and individuals seeking refuge from all of the world's worst conflicts and human disasters. Glasgow is a city that does not walk by on the other side of the road.

There are those who point to the UK government money the city receives to renovate its worst social housing to make it mildly fit for human habitation. Glasgow insists on the children of refugees and asylum seekers being educated alongside our own children, despite being "advised" not to by some Westminster voices. The financial commitment for this – and for providing healthcare and sensitive community policing in the neighbourhoods where they are placed – is substantial and comes from both the city's own budget and from the Scottish government. We reap a rewarding harvest from this, of course.

The influx of these children has led to several threatened primary schools remaining open, while educational and behavioural standards among the children of the host communities have been raised where integration occurs most. Very few other initiatives have made me prouder to be Scottish than this.

Yet while Glasgow, through the superb work of the Scottish Refugee Council, and assorted other third sector and not-for-profit organisations, has stepped up and been counted on this issue, few other local authorities have behaved similarly. Consider Edinburgh, for instance. It's one of the most affluent and privileged cities in Europe, yet you can count the number of refugees and asylum seekers it has agreed to take on the fingers of a packet of shortbread biscuits.

No one is asking our capital city and the other local councils to volunteer to take in thousands. If each of our local authorities agreed even to house a few hundred Syrian refugees for 18 months or so, perhaps until some semblance of normality returns to the region, it would be a start. It would apply pressure on the UK government to agree to take in more of these poor, poor people. If this was copied across Europe and North America, the difference would be meaningful and substantial.

The UK foreign aid minister said last week that government policy is to assist people to remain in their own country as that's better than moving people. But this can't apply in Syria, where we are witnessing the systematic deracination of a people by a regime that appears simply to want to reduce the population size to a more manageable level.

What business is this of ours when we have more than enough social problems of our own? It's the business of common humanity and Glasgow has shown that it is very good at it. Time now for the rest of the country to step up to the mark.