IT is the disconnect that hints of something gone grotesquely wrong, the difference between what one is being told, and what the gut says.

In 2007, when two men drove a car packed with gas canisters into the doors of Glasgow Airport, the first reports described the incident blandly as a "security alert". Then, minute by anxious minute, people inside and outside the terminal, and those stuck on the motorway, on their way to pick up friends and family, began to realise what was happening. Terrorism had come calling, again.

The same air of twisted surreality hung over the streets of Woolwich in south-east London on Wednesday afternoon after a British soldier was hacked to death. In the time it took for police to arrive, one of the alleged attackers addressed an onlooker filming on a mobile phone. Medieval barbarism had met modernity, with profoundly shocking consequences.

Terrorism has its own grisly inflation rate, one that requires each fresh atrocity to be more appalling than the last. Even by these standards, what happened in Woolwich was a landmark moment. There was not the massive loss of life of Lockerbie or the 7/7 bombings in London. Nor was the UK, after decades of The Troubles, a stranger to terrorist attacks. Yet Woolwich, the gut says, merits its own claim to infamy. It was brazen, it was the first attack of its kind on a serving British soldier in the UK, and it appears, from reports so far, to have been home-grown. Those words of hate, spewed into the eye of a mobile phone, were said in a London accent.

What they spoke of were distant wars coming home, of an eye for an eye, a tooth for a tooth, of atrocities never ending as long as British forces, and Western forces in general, were in Islamic lands. Once again, the spectre of perpetual war has been raised, leaving an open, democratic society to wonder how it can possibly deal with such walled-in hatred.

It is a question that is not going away any time soon, and the need for an answer is increasing in urgency. At a Congressional hearing in Washington this week, a Pentagon official estimated that the "war on terror" could last another 10 to 20 years "at least".

It was against this backdrop, and in the aftermath of the Boston marathon bombing, that President Barack Obama was set to outline his administration's response to the continuing threat. Controversial drone strikes, blamed for mass civilian deaths and casualties, will come under stricter rules and control. They will not, one notes, be ended. The closure of Guantanamo, an act pledged during his first term, will continue to be in his sights. On that, and on many another front, mission appeared a very long way from being accomplished.

Here, David Cameron, the Prime Minister, in common with other political leaders, said yesterday that one of the best ways of defeating terrorism was to go about our lives as usual. It has become a truism, but it is an essential one, and each society has its own way of getting back to normal. In Glasgow, such was the way have-a-go-heroes had a go, a certain amount of iron-jawed jocularity took the edge off the shock. This was Glasgow, remember. Mess with our holidays and we'll just set about ye. After 7/7 Londoners also drew strength from a bloody-minded determination that the bloody terrorists would not win.

Then, as now, politicians were quick to stress that such attacks, though they may be carried out by fanatics trying to justify their actions in the name of Islam, have nothing to do with Islam proper. John Reid, the former Defence Secretary, put it best yesterday when he said that the dividing line was not between Islam and non-Islam, but between the terrorists and everyone else. It is a crucial point to emphasise, and not just to head off a violent counter-reaction from thugs on the extreme right.

This is undoubtedly a conflict between "them and us", but so far the terrorists have had it all their own way in defining who belongs to which side and why. We have heard a lot about them, and not enough about us, and the rights and responsibilities that belonging to this side brings. The narrative, as they like to call it in think tanks, has been going the wrong way.

Take Bilal Abdulla, one of the Glasgow Airport attackers, an NHS doctor, no less, who had been born in the UK, and was living and working in Scotland. During his trial he blamed the invasion of Iraq for his actions. Yet many millions of people opposed the war in Iraq. They took to the streets on marches, they wrote to their MPs, they remembered their grievance at the ballot box come election time. They did everything, in short, by the democratic book. They did not stop the war, but nor did terrorism. It has been the passage of time, changes of administration, and soaring costs, that have set in motion the withdrawal of forces from Iraq and Afghanistan. That, in a democracy, is real politik.

One has to wonder, and despair, how anyone can become so alienated from their neighbour, and from the country in which they live, that they would want to lash out in the way we saw at Woolwich this week. Such an atrocity has been anticipated, and indeed similar plots have been foiled in the past, but what the security services did not know was whether it would be perpetrated by individuals acting alone, or as part of the actions of a wider network based abroad.

Either way, what happened at Woolwich will not be prevented in future by the courts, legislation, and security services alone. If this is a home-grown problem then the solution starts at home, too. The process has to begin, as it has done, with all faith groups and none condemning such actions unreservedly. The next part is the toughest: convincing "them" to get on the same side as "us". At the moment, we are only fully engaged in two parts of what has to be a three-pronged strategy. We have prison as a deterrent and we ask the security services to do all they can on prevention. Where we lag behind is on the persuasion front.

What form that persuasion takes, whether it is something as immediate as having a job to get up for in the morning, or as long term as better education, is for another day. What Woolwich showed was that there is a capacity, and a willingness, to do more. The worst of human nature may have been on display that day, but so was the best in the form of what the media likes to call "ordinary people" doing such extraordinary things as approaching armed men and trying to persuade them to hand over their weapons. While instinct might have told many of us to flee the scene, they tried to help. Just as in Glasgow, London, New York, and elsewhere. Try as terrorism might to divide, it is ordinary decency that binds us together.