That’s why the F.B.I.’s profilers have always tried to supplement the basic outlines of the organized/disorganized system with telling details—something that lets the police zero in on a suspect. In the early eighties, Douglas gave a presentation to a roomful of police officers and F.B.I. agents in Marin County about the Trailside Killer, who was murdering female hikers in the hills north of San Francisco. In Douglas’s view, the killer was a classic “disorganized” offender—a blitz attacker, white, early to mid-thirties, blue collar, probably with “a history of bed-wetting, fire-starting, and cruelty to animals.” Then he went back to how asocial the killer seemed. Why did all the killings take place in heavily wooded areas, miles from the road? Douglas reasoned that the killer required such seclusion because he had some condition that he was deeply self-conscious about. Was it something physical, like a missing limb? But then how could he hike miles into the woods and physically overpower his victims? Finally, it came to him: “ ‘Another thing,’ I added after a pregnant pause, ‘the killer will have a speech impediment.’ ”

And so he did. Now, that’s a useful detail. Or is it? Douglas then tells us that he pegged the offender’s age as early thirties, and he turned out to be fifty. Detectives use profiles to narrow down the range of suspects. It doesn’t do any good to get a specific detail right if you get general details wrong.

In the case of Derrick Todd Lee, the Baton Rouge serial killer, the F.B.I. profile described the offender as a white male blue-collar worker, between twenty-five and thirty-five years old, who “wants to be seen as someone who is attractive and appealing to women.” The profile went on, “However, his level of sophistication in interacting with women, especially women who are above him in the social strata, is low. Any contact he has had with women he has found attractive would be described by these women as ‘awkward.’ ” The F.B.I. was right about the killer being a blue-collar male between twenty-five and thirty-five. But Lee turned out to be charming and outgoing, the sort to put on a cowboy hat and snakeskin boots and head for the bars. He was an extrovert with a number of girlfriends and a reputation as a ladies’ man. And he wasn’t white. He was black.

A profile isn’t a test, where you pass if you get most of the answers right. It’s a portrait, and all the details have to cohere in some way if the image is to be helpful. In the mid-nineties, the British Home Office analyzed a hundred and eighty-four crimes, to see how many times profiles led to the arrest of a criminal. The profile worked in five of those cases. That’s just 2.7 per cent, which makes sense if you consider the position of the detective on the receiving end of a profiler’s list of conjectures. Do you believe the stuttering part? Or do you believe the thirty-year-old part? Or do you throw up your hands in frustration?

There is a deeper problem with F.B.I. profiling. Douglas and Ressler didn’t interview a representative sample of serial killers to come up with their typology. They talked to whoever happened to be in the neighborhood. Nor did they interview their subjects according to a standardized protocol. They just sat down and chatted, which isn’t a particularly firm foundation for a psychological system. So you might wonder whether serial killers can really be categorized by their level of organization.

Not long ago, a group of psychologists at the University of Liverpool decided to test the F.B.I.’s assumptions. First, they made a list of crime-scene characteristics generally considered to show organization: perhaps the victim was alive during the sex acts, or the body was posed in a certain way, or the murder weapon was missing, or the body was concealed, or torture and restraints were involved. Then they made a list of characteristics showing disorganization: perhaps the victim was beaten, the body was left in an isolated spot, the victim’s belongings were scattered, or the murder weapon was improvised.

If the F.B.I. was right, they reasoned, the crime-scene details on each of those two lists should “co-occur”—that is, if you see one or more organized traits in a crime, there should be a reasonably high probability of seeing other organized traits. When they looked at a sample of a hundred serial crimes, however, they couldn’t find any support for the F.B.I.’s distinction. Crimes don’t fall into one camp or the other. It turns out that they’re almost always a mixture of a few key organized traits and a random array of disorganized traits. Laurence Alison, one of the leaders of the Liverpool group and the author of “The Forensic Psychologist’s Casebook,” told me, “The whole business is a lot more complicated than the F.B.I. imagines.”

Alison and another of his colleagues also looked at homology. If Douglas was right, then a certain kind of crime should correspond to a certain kind of criminal. So the Liverpool group selected a hundred stranger rapes in the United Kingdom, classifying them according to twenty-eight variables, such as whether a disguise was worn, whether compliments were given, whether there was binding, gagging, or blindfolding, whether there was apologizing or the theft of personal property, and so on. They then looked at whether the patterns in the crimes corresponded to attributes of the criminals—like age, type of employment, ethnicity, level of education, marital status, number of prior convictions, type of prior convictions, and drug use. Were rapists who bind, gag, and blindfold more like one another than they were like rapists who, say, compliment and apologize? The answer is no—not even slightly.

“The fact is that different offenders can exhibit the same behaviors for completely different reasons,” Brent Turvey, a forensic scientist who has been highly critical of the F.B.I.’s approach, says. “You’ve got a rapist who attacks a woman in the park and pulls her shirt up over her face. Why? What does that mean? There are ten different things it could mean. It could mean he doesn’t want to see her. It could mean he doesn’t want her to see him. It could mean he wants to see her breasts, he wants to imagine someone else, he wants to incapacitate her arms—all of those are possibilities. You can’t just look at one behavior in isolation.”

A few years ago, Alison went back to the case of the teacher who was murdered on the roof of her building in the Bronx. He wanted to know why, if the F.B.I.’s approach to criminal profiling was based on such simplistic psychology, it continues to have such a sterling reputation. The answer, he suspected, lay in the way the profiles were written, and, sure enough, when he broke down the rooftop-killer analysis, sentence by sentence, he found that it was so full of unverifiable and contradictory and ambiguous language that it could support virtually any interpretation.

Astrologers and psychics have known these tricks for years. The magician Ian Rowland, in his classic “The Full Facts Book of Cold Reading,” itemizes them one by one, in what could easily serve as a manual for the beginner profiler. First is the Rainbow Ruse—the “statement which credits the client with both a personality trait and its opposite.” (“I would say that on the whole you can be rather a quiet, self effacing type, but when the circumstances are right, you can be quite the life and soul of the party if the mood strikes you.”) The Jacques Statement, named for the character in “As You Like It” who gives the Seven Ages of Man speech, tailors the prediction to the age of the subject. To someone in his late thirties or early forties, for example, the psychic says, “If you are honest about it, you often get to wondering what happened to all those dreams you had when you were younger.” There is the Barnum Statement, the assertion so general that anyone would agree, and the Fuzzy Fact, the seemingly factual statement couched in a way that “leaves plenty of scope to be developed into something more specific.” (“I can see a connection with Europe, possibly Britain, or it could be the warmer, Mediterranean part?”) And that’s only the start: there is the Greener Grass technique, the Diverted Question, the Russian Doll, Sugar Lumps, not to mention Forking and the Good Chance Guess—all of which, when put together in skillful combination, can convince even the most skeptical observer that he or she is in the presence of real insight.