In a dogged attempt at an upbeat tone, the reports have homed in on the tiny band of survivors, spiralling their way down the internal staircases as the towers burnt their way towards collapse: small tales of bravery that only demonstrate how survival was entirely down to chance.

The message of these stories, and of the flood of sober analyses that has poured out before the fifth anniversary, has been that the world is now a more threatening place. A “new” threat of Islamic terrorism, which had not touched the lives of many in the West before 9/11, now seems everywhere; we are fighting a “War on Terror”, and we are losing. In some broad sense, they argue, the world is more dangerous, its threats more connected; we are worse off than the innocents before 9/11.

I don’t think that is true, understandable though the feelings are. There is a strong case for optimism: that the world is faring better than before 9/11, and that there are good reasons for this to continue.

That is not principally because of governments’ responses to 9/11, I should say, although those may bear more fruit than they yet have. The threat of Islamist terrorism has not diminished.

But huge changes for the good more than counterbalance the destruction and despair in parts of the Middle East: in China, in India, in Eastern Europe, in the vitality of the US itself. Those have transformed the lives of their own people, within a few years, and offer the hope that countries now battling against extremism will find their way out.

Let me make a batch of concessions up front. I would agree that malevolence in far-off places now feels intimate because of 21st-century transport and communications. The Torkhum Gate, at the end of the Khyber Pass, marks the point where Pakistan’s wild tribal lands give way to Afghanistan. Its stumpy towers, like a child’s effort to make a castle out of too few pieces of Lego, are a gesture at a border that is otherwise non-existent.

Somewhere in the 300 miles of mountains to the south, Osama bin Laden is hiding, according to US intelligence and President Musharraf of Pakistan. Yet this lawless region, where the 9/11 attacks were devised, and which, through nearby madrassas, may have inspired some of the July 7 bombers on the London Underground, is reachable with an eight-hour flight from London, plus an eight-hour drive.

In answer to the bald question “are we (say, in London) more likely to be attacked by Islamic terrorists than before 9/11?”, I would have to answer yes. The ambition and success of the 9/11 attacks inspired others (such as last month’s alleged plot to blow up trans-atlantic flights from Heathrow). Our illustration shows attacks attributed to al-Qaeda since 9/11; they cover the globe.

For all the apparent success of Western intelligence agencies in thwarting new terrorist plots, there is an almost comic sense that, like the sheriffs of the Wild West, they hope that by locking up the few bad men they will solve the problem.

The risk instead is that they may help it to proliferate. It is foolish to deny that the US’s poor judgment in Iraq, and its inability to quell the violence, will have inspired more jihadists. That has clearly invigor- ated Iran, too, whose nuclear ambitions remain uncurbed.

The US’s abuse of its own principles of human rights and justice at Abu Ghraib and Guantanamo Bay have compromised its claim to be fighting in their name. Its impatience with both the United Nations and international law has exposed their deficiencies.

It has become fashionable to portray all these threats as linked, spinning out to encircle the planet: from al-Qaeda, to Iraq, to Iran, through nuclear proliferation, to energy security. The vocabulary of President Bush and Tony Blair — the “War on Terror” above all — reflects the same impulse.

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