We watch their movies, we eat their fast food. Their culture has become global culture. So it always comes as a shock to realise how different Americans are from everyone else. The massacre in Newtown horrified even those who thought themselves inured to horror – I know many who could hardly bear to look at those smiling family photographs of the children – but for non-Americans the subsequent discussion has also been shocking to watch.

To outsiders, the point seems so blindingly obvious: more guns equal more death. In Britain, where gun laws are strict, the annual number of gun-related murders stood, at last count, at 41. In the US the equivalent figure is just short of 10,000.

Whether it's Britain, Japan or Australia, the evidence is the same: strict gun control means fewer people die. American unwillingness to face this basic arithmetic – preferring to blame the mental health system or videogames or the "feminisation" of the classroom, as one conservative pundit did, or the absence of religious prayer in schools – the explanation of former Republican presidential candidate Mike Huckabee – rather than the most obvious culprit for all this gun violence, namely easy access to military-grade assault weapons, can drive outsiders to distraction. Witness Piers Morgan's bad-tempered hosting of a CNN debate on guns this week, haranguing his guests for failing to admit what to him was obvious – a performance that few of his American colleagues would match.

What exactly is America's problem? Why does it stand so far apart, notching up more gun homicides than the rest of the world's wealthy countries put together? People like to point the finger at the mighty National Rifle Association, which, to be sure, is a well-funded, effective lobby, especially in battleground congressional districts where NRA members can make the difference between victory and defeat. But big tobacco used to be a mighty lobby too; yet when the evidence linked smoking to lung cancer, they were steadily beaten back. Judging by its abysmal performance at a bizarre press conference today, the NRA could ultimately be defeated.

If you really want to know why the US can't kick its gun habit, take a trip to the National Archives in Washington, DC. You don't even have to look at the exhibits. Just study the queue. What you'll see are ordinary Americans lining up, in hushed reverence, to gaze at an original copy of the United States constitution, guarded and under heavily armoured glass. It is no exaggeration to say that for many Americans this is a religious experience.

When outsiders hear that the right to bear arms is enshrined in the second amendment of the US constitution, I suspect many imagine this is like saying it's "protected by law", something that can easily be changed, as it would be in their own countries. But this is to underestimate what the constitution means to Americans.

It is indeed a sacred text. Despite, or perhaps because, the US is a country animated by faith, the "founding fathers" are treated as deities, their every word analysed as if it contained gospel truth. Any new idea or policy proposal, no matter how worthy on its own merits, must be proven compatible with what those long-dead politicians of the late 18th century set down – otherwise it's unconstitutional and can be thrown out by the supreme court, the high priesthood selected to interpret what the great prophets of Philadelphia intended.

I don't mock America's awe for its constitution. On the contrary, I regard that text as the most powerful statement of democratic principle – starting with its declaration that "we the people" are sovereign – and human rights ever written. Its system of checks and balances is mathematically and beautifully precise in its determination to prevent unfettered, over-centralised power. It represents the unfinished business of England's own incomplete revolution of 1688. It's no exaggeration to say that this single document makes the US possible, cohering an immigrant nation with no common bonds of blood or soil around a radical idea.

But when the attachment to that text calcifies into a rigid dogma, danger beckons. Even the best ideals can become warped: note how the first amendment guarantee of free speech has allowed unlimited spending on TV campaign ads by anonymous corporate donors. In the case of the second amendment, a constitution designed to be a document of liberation instead imprisons the US, shackling it to an outdated rule that makes easy the murder of schoolchildren. Polls show a majority of Americans favour greater gun control, but the US constitution stands stubbornly in their way. The scholar Daniel Lazare describes America as "the frozen republic", chained to decisions taken when the right to bear arms meant the freedom to carry a musket. He wants the US to revamp its constitution, like most of the other countries of the world: "Why must Americans remain slaves to the past?"

Absent a cataclysm, such as the US suffering a total defeat in war, it's hard even to imagine such a thing. But that does not render gun control advocates powerless. Change is possible even within the constitution. It's worth remembering that it was only by a 5-4 margin that the nine judges of the supreme court ruled in 2008 that the second amendment applied to individuals at all; until then, the court held for decades that the constitution protected only the right of a "well-regulated militia" to bear arms. Admittedly, scholarly opinion has steadily moved towards the individualist reading, but it is at least theoretically possible that, with a new judge or two, that 5-4 majority could flip the other way.

Failing that, there is scope to change the sacred text itself. It's extremely hard – requiring two-thirds majorities in Congress and three-quarters of the state legislatures – but it's not impossible. The clue is in the name: the second amendment. The constitution can and has been amended, whether to abolish slavery, grant votes for women, or (in 1920) to prohibit alcohol, the last of these repealed just 13 years later. Each of these would have seemed impossible at the time; the first came at the price of a civil war. But if the political will is there, it can be done. America need not be frozen. On the contrary, it was founded on the ideal that each generation is able to make the world anew.

If Americans truly want to see an end to horrors like the one that took the children of Newtown, they ought to heed the words of that great British-born hero of the American revolution, Thomas Paine: "The circumstances of the world are continually changing, and the opinions of men change also," he wrote. "Government is for the living, and not for the dead; it is the living only that has any right in it."

Twitter: @j_freedland