One of my special interests is serial killers. The author of that book had a lot of uncorrected errors in regards to the alleged AS serial killers--- spelling their names wrong, getting events wrong. I got the impression that he only read one book on each case, and not very carefully.
That being said, I think some serial killers such as Dahmer and Gein did have symptoms of AS. Hey, if neurotypicals can serial-kill, we can serial-kill.
As for the lack of empathy thing: both sociopaths and people with AS are said to lack 'empathy'. In the case of people with AS, I think it is that we don't pick up the non-verbal clues that show us the emotional states of others, and therefore, being unaware, we don't share the emotions of others and in that sense lack empathy. In my own case, when I do become aware of someone's emotions, I do empathize.
In the person who is a sociopath and does not also have AS, it's perhaps not a matter of not picking up non-verbal clues from others, but of not caring enough about others to have empathy.
In other words, the lack of empathy in AS is a lack of informed empathy, while the lack of empathy in sociopathy is a 'don't care' lack of empathy.
I'm wondering if it is possible for a person to have both AS and be a sociopath--- perhaps that would explain some of the cases of serial killers alleged to have AS better than the idea of having a 'killer' variant of AS.
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