NEW YORK • The brothers who carried out suicide bombings in Brussels last week had long, violent criminal records and had been regarded internationally as potential terrorists.
But in San Bernardino, California, last year when 14 people were killed and 22 seriously injured in a mass shooting by a married couple, one of the attackers was a county health inspector who lived a life of apparent suburban normality.
Of the dozens of other young American men and women arrested over the past year for trying to help the Islamic State in Iraq and Syria (ISIS), their backgrounds are so diverse that they defy a single profile.
What turns people towards violence - and whether they can be steered away from it - are questions that bedevil governments around the world. Those questions have taken on fresh urgency with the rise of ISIS and the string of attacks in Europe and the US.
When researchers do come up with possible answers, the government often disregards them.
Not long after the attacks of Sept 11, 2001, Professor Alan B. Krueger, a Princeton economist, tested the widespread assumption that poverty was a key factor in the making of a terrorist. His analysis of economic figures, polls, and data on suicide bombers and hate groups found no link between economic distress and terrorism.
Yet more than a decade later, US law enforcement officials and government-funded community groups still regard money problems as an indicator of radicalisation.
And many studies seem to warn of the adolescent condition, singling out young, impatient men with a sense of adventure "struggling to achieve a sense of selfhood".
Such generalisations are why civil libertarians see only danger in government efforts to identify people at risk of committing crimes.
Researchers, too, say they have been frustrated by both the Bush and Obama administrations because of a preoccupation with research that can be distilled into simple checklists, even at the risk of casting suspicion on innocent people.
"The people with guns and badges are so eager to have something. The fact that they could actually do harm? This doesn't deter them," said Prof Clark R. McCauley Jr, a professor of psychology at Bryn Mawr College who has conducted government-funded terrorism research for years.
Though the government plays down its use of checklists, the US Justice Department offers grants for the development of "a rapid assessment" tool to help "gauge the potential" for extremism.
Last year, the Intercept news organisation revealed a government checklist to score people in terrorism investigations, based on factors, including whether they feel mistreated by the government, distrust law enforcement or suffer from discrimination.
As a practical matter, scientists note, checklists are mathematically certain to fail. Even a test with 99 per cent accuracy would be wrong far more often than right. In a country with a huge population and a tiny number of terrorists, even a near-perfect test would flag many more innocent people than actual terrorists.
Europe, too, is grappling with these questions. In Britain, the government encourages or requires people to alert the authorities about people who could become risks. That has raised questions in the US about whether the Constitution would allow the government to keep tabs on lawful political or religious speech.
Researching terrorism also involves tough questions about who qualifies as a terrorist, or as a rebel or a soldier. Nelson Mandela? Palestinian suicide bombers? The Taleban of today? The Afghan mujahideen when the CIA supported them?
When the US government does give advice about what to look for, the origin of that information is often impossible to know. A 2012 National Counterterrorism Centre report, for instance, declared that anxiety, unmet personal needs, frustration and trauma helped drive radicalisation.
"Not all individuals who become radicalised have unmet personal needs, but those who do are more vulnerable to radicalisation," the document said, citing no sources.
Researchers seldom have access to terrorists, and scientific methods, such as control groups, are rare.
Dr Jeff Victoroff, a University of Southern California psychologist, concluded that the leading terrorism research was mostly just political theory and anecdotes.
"A lack of systematic scholarly investigation has left policymakers to design counterterrorism strategies without the benefit of facts," he wrote in The Journal of Conflict Resolution in 2005.
NEW YORK TIMES