Jamie Bartlett, head of the Violence and Extremism program at the think tank Demos, echoes these doubts. "The word 'radicalization' suggests a fairly simple linear path toward an ultimate violent conclusion," he says.
Studies suggest that although there may be stages in the evolution of a terrorist, placing them sequentially on a line, as the NYPD's report literally does, is far too pat. The stages are fluid, not a simple trajectory, and it is virtually impossible to predict who will or won't engage in violence based solely on their beliefs.
"I have found that many young home-grown al-Qaeda terrorists are not attracted by religion or ideology alone – often their knowledge of Islamist theology is wafer-thin and superficial – but also the glamour and excitement that al-Qaeda type groups purports to offer," Bartlett notes.
When it comes to why someone chooses to engage in terrorism, Horgan says, "there are the bigger social, political and religious reasons people give for becoming involved" – for instance, anger over government policies or a foreign occupation. But that leaves out a key part of the story.
"Hidden behind these bigger reasons, there are also hosts of littler reasons – personal fantasy, seeking adventure, camaraderie, purpose, identity," adds Horgan. "These lures can be very powerful, especially when you don't necessarily have a lot else going on in your life, but terrorists rarely talk about them."