After a horrific massacre such as the one in Newtown, Connecticut, the word “senseless” gets a lively airing. Public commentators in America who otherwise deliver the most vituperative and screeching content will hush their voices to deliver sad sermons of resignation. It’s just the inevitable and inscrutable nature of things (they explain) for evil to erupt at intervals. There is nothing to be said and nothing to be done.

This is all untrue. There is a lot that might be said to explain the American propensity for mass killing. There is a lot that could be done to reduce the frequency and lethality of such crimes. The message of sorrow is intended not to console but to conceal — to divert attention from the public policy choices that enabled the Connecticut killer to break the heart of a whole town.

The non-secret of American gun violence is contained in three seeming paradoxes.

Paradox 1: Random outbursts of stranger violence happen everywhere in the world. Only in America do they regularly leave dozens dead.

Paradox 2: Since 1990 American crime rates in general have radically declined. Yet gun massacres seem to have increased in frequency.

Paradox 3: In the 1990s the proportion of Americans who kept a gun in their home fell from one half to one third. Yet even as gun ownership has declined, opposition to gun control has strengthened.

The key to unlock paradox 1 is this knowledge: people are driven to stranger violence by recognisable forms of mental illness. These mental illnesses occur in people of all countries. A Wikipedia page records school attacks in China. There have been at least nine since March 2010, including an especially savage attack on the very day of the Newtown massacre. Yet the total death toll from all these attacks, in a much more populous country than the United States, is less than the one-day toll in Newtown. Chinese attacks are carried out with knives or sometimes axes, not guns.

Australia, a country in many ways culturally similar to the United States, banned semi-automatic weapons in 1996. The government instituted a programme to buy guns from owners. Result: Australia suffered 13 mass shootings in the years 1978-96 and has suffered zero in the years since.

More ominous still, the guns available to private Americans have become dramatically deadlier over the past generation. In the 1980s the majority of guns in private hands in the United States were revolvers: guns that fired six or seven shots between reloads. Now the gun market is dominated by semi-automatic weapons that can be equipped with extended magazines holding up to 100 rounds.

To unlock paradox 2, consider this: Mother Jones magazine has tallied all the mass casualty shootings of the past 30 years: 62 in all. Of those 62, 25 have occurred since 2006. This year alone there have been seven mass shootings, including Newtown’s Sandy Hook Elementary School. Like everything else in our society, the idea of mass shootings is spread faster in the era of cable news and social media.

Conventional murder, robbery and other crimes are susceptible to prevention by good police work and deterrence by punishment. The people who commit massacres, however, do not fear getting caught. They typically expect to die in the course of their attack, cut down either by police or by their own hand.

It is mental health systems that must stop them, if they are to be stopped — and mental health services in the United States are both threadbare and lacking in power to compel treatment.

To resolve paradox 3, you need to understand a change in the reasons for gun ownership. Fifty years ago, Americans associated legitimate gun ownership with the sport of shooting. Handguns and rapid-fire weapons were seen as arms for criminals. Public opinion supported laws against such weapons. In 1934 the United States heavily restricted the automatic weapons associated with the gangsters of Prohibition times; in 1968 America acted against the handguns associated with the era’s rise in street crime.

As the United States has become more urbanised, hunting has faded as a recreation. In 2011, less than 5% of the population went hunting. Today’s gun owner is less likely to be a sportsman than a middle-aged suburbanite haunted by fears of crime.

In the words of the Tennessee lawmaker who introduced the law allowing guns to be carried into his state’s bars: “Folks were being robbed, assaulted — it was becoming an issue of personal safety. The police aren’t going to be able to protect you. They’re going to be checking out the crime scene after you and your family’s been shot or injured or assaulted or raped.”

Those fears of crime are increasingly disconnected from reality in today’s safer America. The overall violent crime index has tumbled by a third since the early 1990s. The worst crimes — murder and rape — have declined even more. American citizens are safer from crime today than at almost any time since record-keeping began.

That is not how Americans see things, however. They perceive a country of increasing rather than decreasing danger and more and more of them espouse an ideology of self-help in the face of those imaginary threats.

Gun advocates cite a statistic that guns are used in self-defence 2.5m times a year. That statistic is based on surveys conducted in the early 1990s. It relied on respondents’ own memories of their gun use over long periods of time, an invitation to distortion and exaggeration. It drew no distinction between a gun used against an intruder and a gun carried while investigating strange scratching noises in the garage.

The number is not taken seriously by social science researchers and yet it is exhibit A in favour of the “concealed carry” laws that will soon be on the books of every one of the 50 states.

As for the idea that armed civilians might stop gun massacres, it is a fantasy, plain and simple. As Mother Jones reports: “Gun rights die-hards frequently credit the end of a rampage in 2002 at the Appalachian School of Law in Virginia to armed ‘students’ who intervened — while failing to disclose that those students were also current and former law enforcement officers and that the killer, according to police investigators, was out of ammo by the time they got to him.”

In all the many massacres of the past 30 years only one perpetrator was stopped by an armed civilian, back in 1982 — and only after the killer had completed his spree and left the scene.

The ideal of guns as self-protection owes little to evidence and much to the kind of cultural fears that have come into greater visibility since the election of President Barack Obama.

Four days before the shooting in Newtown, an advertiser in the conservative National Review sent the following email to subscribers: “Since the 1970s the bleeding-heart liberals in Washington have let this all happen … They’ve been hell-bent on passing laws that legally empower dangerous criminals; including reduced sentences, minimal jail time and easy parole. While at the same time literally castrating law-abiding citizens like you and me whenever we attempt to defend ourselves, our home and our family.”

None of those claims is true, of course. American prison sentences are the most draconian in the democratic world. Yet those claims find ready credence. They are the emotions that inhibit the rational regulation of firearms — and that enable atrocities such as the massacre in Newtown to recur again and again and again.