In normal members of the population, theta waves are associated with drowsy, meditative or sleeping states. Yet in psychopaths they occur during normal waking states - even, sometimes, during states of increased arousal...
"Language, for psycopaths, is only word deep. There's no emotional contouring behind it. A psycopath may say something like "I love you", but in reality it means about as much to him as if he said "I'll have a cup of coffee"... This is one of the reasons psychopaths remain so cool, calm and collected under conditions of extreme danger, and why they are so reward-driven and take risks. Their brains, quite literally, are less "switched on" than the rest of ours."

The observation that modern-day humans are pathologically risk averse does not, needless to day, mean that this has always been the case. In fact, it might even be argued that those of us today who are clinically risk averse - those of us, for instance, who suffer from chronic anxiety - simply have too much of a good thing. During the time of our ancestors the existence of individuals who were hypervigilant to threat may well, evolutionary biologists suggest, have been decisive in the fight against predators - and from this point of view, anxiety would undoubtedly have served as a considerable adaptive advantage. The more sensitive you were to rustlings in the undergrowth the more likely you'd have been to have kept yourself, your family and your extended group members alive. Even today, anxious individuals are better that the rest of us at detecting the presence of threat: slip an angry face in among a display of happy or neutral faces on a computer screen, and anxious people are far faster at picking it out than those who are non-anxious - not a bad ability to fall back on should you happen to find yourself alone at night and wandering around an unfamiliar neighbourhood. Being anxious can sometimes be useful.

As one hugely successful young attorney told me on the balcony of his penthouse apartment overlooking the Thames: "Deep inside me there's a serial killer lurking somewhere. But I keep him entertained with cocaine, Formula One, booty calls and coruscating cross-examination."
Ever so slowly, I moved away from the edge.
This aerial encounter with the young lawyer (he later ran me back to my hotel down river in his speedboat) goes some way towards illustrating a theory I have about psychopaths: that one of the reasons we're so fascinated by them is because we're fascinated by illusions, by things that appear, on the surface, to be normal, yet that on closer examination turn out to be anything but.

"People think [psychopaths] are just callous and without fear," he says. "But there is definitely something more going on. When emotions are their primary focus, we've seen that psychopathic individuals show a normal [emotional] response. But when focused on something else, they become insensitive to emotions entirely."

In a survey which has so far tested 14,000 volunteers, Konrath has found that college students' self-reported empathy levels (as measured by the Interpersonal Reactivity Index) have actually been in steady decline over the previous three decades - since the inauguration of the scale, in fact, back in 1979. And that a particularly pronounced slump has, it turns out, been observed over the past ten years.
"College kids today are about 40 per cent lower in empathy than their counterparts of twenty or thirty years ago," Konrath reports. More worrying still, according to Jean Twenge, professor of psychology at San Diego State University, is that, during this same period, students' self-reported narcissism levels have, in contrast, gone in the other direction. They've shot through the roof.

My old man was a psychopath. It seems a bit odd saying that now, looking back. But he was. No question. He was charming, fearless, ruthless (but never violent). And had about as much going on in the conscience department as a Jeffrey Dahmer coolbox. He didn't kill anyone. But he certainly made a few killings.

The notion that mental disorder can occasionally come in handy, can sometimes confer extraordinary, outlandish advantages, as well as an inordinate distress on its sufferers, is hardly new, of course. As the philosopher Aristotle observed more than 2,400 years ago, "There was never a genius without a tincture of madness."

When you go down the road of disorders conferring advantages, of clouds, silver linings and psychological consolation prizes, it's difficult to conceive of a condition that doesn't pay off - at least in some form or another. Obsessive-compulsive? You're never going to leave the gas on. Paranoid? You'll never fall foul of the small print. In fact, fear and sadness - anxiety and depression - constitute two of the five basic emotions that have evolved universally across cultures and that, as such, virtually all of us experience at some point in our lives. But there's one group of people who are the exception to the rule, who don't experience either - even under the most difficult and trying circumstances. Psycopaths. A psycopath wouldn't worry even if he had left the gas on. Any silver linings there?
Put this question to a psychopath and, more often than not, he'll look at you as if you're the one who's crazy. To a psychopath, you see, there are no such things as clouds. There are only silver linings.

A scorpion and a frog are sitting on the bank of a river and both need to get to the other side.
"Hello, Mr Frog!" calls the scorpion through the reeds. "Would you be so kind as to give me a ride on your back across the water? I have important business to conduct on the other side. And I cannot swim in such a strong current."
The frog immediately becomes suspicious.
"Well, Mr Scorpion," he replies, "I appreciate the fact that you have important business on the other side of the river. But take just a moment to consider your request. You are a scorpion. You have a large stinger at the end of your tail. As soon as I let you onto my back, it is entirely within your nature to sting me."
The scorpion, who has anticipated the frog's objections, counters thus:
"My dear Mr Frog, your reservations are perfectly reasonable. But it is clearly not in my interest to sting you. I really do need to get to the other side of the river. And I give you my word that no harm will come to you."
Reluctantly the frog agrees that the scorpion has a point. So he allows the fast-talking anthropod to scramble atop his back. And hops, without any further ado, into the water. At first, all is well. Everything goes exactly according to plan. But halfway across, the frog suddenly feels a sharp pain in his back - and sees, out of the corner of his eye, the scorpion withdraw his stinger from his hide. A deadening numbness begins to creep into his limbs.
"You fool!" croaks the frog. "You said you needed to get to the other side to conduct your business. Now we are both going to die!"
The scorpion shrugs. And does a little jig on the drowning frog's back.
"Mr Frog," he replies casually, "you said it yourself. I am a scorpion. It is in my nature to sting you."
With that, the scorpion and the frog both disappear beneath the murky, muddy waters of the swiftly flowing current.
And neither of them is seen again.

During his trial in 1980, John Wayne Gacy declared with a sigh that all he was really guilty of was "running a cemetery without a license."