Statisticians Uncover the Mathematics of a Serial Killer 164
Hugh Pickens writes writes "Andrei Chikatilo, 'The Butcher of Rostov,' was one of the most prolific serial killers in modern history committing at least 52 murders between 1978 and 1990 before he was caught, tried, and executed. The pattern of his murders, though, was irregular with long periods of no activity, interrupted by several murders within a short period of time. Hoping to gain insight into serial killings to prevent similar murders, Mikhail Simkin and Vwani Roychowdhury at UCLA built a mathematical model of the time pattern of the activity of Chikatilo and found the distribution of the intervals between murders follows a power law with the exponent of 1.4. The basis of their analysis is the hypothesis that 'similar to epileptic seizures, the psychotic affects, causing a serial killer to commit murder, arise from simultaneous firing of large number of neurons in the brain.' In modeling the behavior the authors didn't find that 'the killer commits murder right at the moment when neural excitation reaches a certain threshold. He needs time to plan and prepare his crime' so they built delay into their model. The killings eventually have a sedative effect, pushing the neuronal activity below the 'killing threshold' – which is why there are large intervals of time between groups of murders. 'There is at least qualitative agreement between theory and observation [PDF],' conclude the authors. 'Stats can't tell you who the perp is, but they're getting better and better at figuring out where and when the next crime might happen,' writes criminal lawyer Nathaniel Burney adding that 'catching a serial killer by focusing resources based on when and where he's likely to strike next is a hell of a lot better than relying on the junk science of behavioral profiling.'"
Great. So now all we need... (Score:5, Insightful)
...is another series of murders to consolidate the theory.
Any takers?
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Okay. I'll do it. It'll only be four people, though, is that enough? I hope so.
Re:Great. So now all we need... (Score:5, Funny)
I wonder if it also correlates to how often you post on Slashdot. We don't know who you are AC, but we know when you'll strike next.
Re:Great. So now all we need... (Score:5, Interesting)
Exactly. This whole hypothesis is based on one data point alone. There were more than one serial killers, why did they try their hypothesis on just this one? Or was he the only one who fit in the equation?
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They need more than just another series of murders... They need to have all the murders (I.E. bodies found after a delay will skew the data) and have them correctly attributed to the proper murderer (both missing and extraneous murders will skew the data). I.E. someone like Gary Ridgeway or Ted Bundy will likely either escape detection entirely or have wildly incorrect predictions. Not to mention killers like BTK who stopped entirely...
Re:Great. So now all we need... (Score:4, Funny)
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And all he has to do is completely mess up the statistics and he could make a killing!
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Exactly. You can fit anything to a given set of data to show some sort of correlation
Sounds like science to me.
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We call that 'soft science,' as opposed to the 'hard science' variety.
Guess which one scientists have in mind when they are talking about "understanding things?"
And for a bonus point, guess which one politicians use when trying to craft a new law?
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so it was the mathamatician (Score:2)
They have 1 data point (Score:5, Insightful)
Aren't they jumping the gun a bit?
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Good sir, allow me to nitpick.
They have more than one data point. What they have is one data set.
Thank you and good day.
Since their model is designed to predict behavior, and it is based on past behavior of one individual, they have precisely one data point.
The thing beind modeled is the pattern of time between killings. Nothing with the individual killings is being modeled.
always some correlation to a single set of data (Score:5, Insightful)
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The question in science has always been, "does it have predictive power?"
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It can if you reapply the trick of staring hard enough at the experiment output until you see the desired result.
Re:always some correlation to a single set of data (Score:5, Insightful)
True. The power law, though, is a particularly dangerous and entrancing trap to fall in to. Almost everything in nature - from pure randomness to highly structured effects - can be fitted to a power law. You often don't even need to do any transformation of the data - simply choosing the wrong set of dependent and independent variables to examine can do it.
My favourite goto whenever this subject comes up is the essay "So You Think You Have a Power Law - Well Isn't That Special?" [umich.edu]
That said, I haven't read the current paper. They might have been very careful to avoid the common traps. I won't know until I spend some time tomorrow reading it.
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A bit hand-wavey? You're being kind. Large groups of neurons collaborating to trigger a single event have been proposed to model precise timing, e.g. in movement, and locking behavior has been observed for speeds in the order of 100Hz to 5Hz, but synchronization over such a long period of time? And large groups? You would think that would be totally impossible. It sounds like
1. We don't know how a large group of neurons behave over long periods
2. We don't know what triggers a serial killer
3. ?
4. Publication
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Whether the distribution is precisely power law or exponential really doesn't really matter that much. With only 52 data points and anything more than trivial noise in the data, every model is going to be an approximation, right?
The bit of profound observation in the paper is surely that there is an aperiodic temporal pattern, and therefore a skewed distribution, that can be modelled with some accuracy. For one killer. And we all know, or should know, the dangers of generalizing from a single example.
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Thanks for that link. I subscribed to the "Three-Toed Sloth" feed.
I like the hopeful conclusion:
"I trust that I will no longer have to referee papers where people use GnuPlot to draw lines on log-log graphs, as though that meant something, and that in five to ten years even science journalists and editors of Wired will begin to get the message. "
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Too little data, and not useful for prediction (Score:3, Informative)
The 'murder probability' comes from a probability density function spanning three years, and is estimated from 53 data points, all from the same subject. That is hardly reliable.
And if we take the sparsity of the data for granted, what is the conclusion? That the less frequently the murderer acts, the less likely he is to act, and vice versa. It is a descriptive model, you can not predict the time of the next murder with it.
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Power law not usefully predictive in this case (Score:5, Insightful)
I think the importance of what they found is overstated. The fact that a murderer's patterns fit a power law is not particularly helpful in really pinning down the time of the next murder. "The expected time of the next murder is a distribution of odds along this curve" is not particularly useful in trying to stop a single crime. Power laws are more useful predictors when applied across populations.
While unlikely to ever be predictive, this result is more interesting from a more academic perspective. It could help illuminate what might be going on in the brain of a serial murderer. Learning how damaged brains function (or fail to function) has long been a means of studying how non-damaged brains may work.
So this might provide some insight into how a compulsive thought builds up in the brain, but it's unlikely to ever allow a profiler to say "stake out this intersection on this night".
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That is true, but it could potentially be useful in linking murders to the same killer, in cases where the link otherwise might not have been made.
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How to derive location though? (Score:2)
knowing a likely area within a couple of suburbs and a time within a couple of months could well be enough for police run undercover operations.
It sure could.
I saw no indication even IF they could predict when a murderer might strike next, they would have any idea whatsoever as to location.
I see no useful narrowing down at all even if they manage to refine the technique.
This really isn't new to The Police (Score:3)
"junk science" of behavioral profiling (Score:5, Insightful)
For behavioral profiling being a "junk science" they've had a lot of successes, and more success than this idea will ever yield (especially since it's so easily reverse engineerable, not to mention vague in its predictions). And the criticism coming from a criminal lawyer - well, I think the lady doth protest too much.
The basic idea of profiling is to narrow a large search down into a smaller one. The basis of the idea that by studying known offenders and finding commonalities between them, you'll have a clue as to the sort of person a perpetrator will be given an arbitrary new crime. Now that enough information about profiling is out there, offenders can and do reverse engineer the profiling process to make it tougher for them to get caught (assuming they are smart enough to do so - many are not that smart). However, at the very least there will be certain things that they are compelled to do otherwise the crime is simply not interesting for them to do. And certain things they have to do to carry out their crimes which will give a clue as to who they are.
The way I look at it, the people who study these particular criminals and offer advice for catching them are analogous to specialist doctors. For example, if you are trying to diagnose and treat some specialist skin condition that is very rare, you will have better results with a referral to a dermatologist than having the GP struggle and try to treat it as best he can.
Re:"junk science" of behavioral profiling (Score:5, Insightful)
Actually, profiling has been seriously challenged, there's a nice New Yorker article [newyorker.com] about it, and several scholarly papers [anu.edu.au], Alison L and Rainbow L. eds (2011) 'Professionalizing Offender Profiling: Forensic and Investigative Psychology in Practice'. Routledge, London. The charge is that profiling is similar to astrology, make vague claims that could match a variety of scenarios, and pay attention when it fits, not when it doesn't.
Like a lot of forensic techniques, it seems to have jumped from the theoretically plausible to practice, without going through the intermediate step of check that it works. "Junk science" may be a fair characterisation.
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Mod parent up. I don't know whether profiling works or not, but that final comment was certainly tacked on without justification.
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The General Practitioner, however, does serve a purpose. He / She has general knowledge of a multitude of diseases, forming a kind of filter, that if he can't treat a disease, he can generally point you in the right direction (refer you to a specialist who may have better equipment / knowledge for a better diagnosis). If medical specialists are encyclopedic albums, then the General Practitioner typically serves the role of the index.
You don't want to be treated by a dermatologist if you need an oncologist.
A
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I agree. It sounds to me like the author has an axe to grind.
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Citation needed. The last estimate I read was something like a 5% success rate. I used that to make fun of Criminal Minds tv show, which has a near 100% success rate. That's the way profilers want to be seen, but it doesn't work out like that. So if you have numbers, preferably in percentages rather than total successes with no context, that would be a good start.
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Citation needed. The last estimate I read was something like a 5% success rate. I used that to make fun of Criminal Minds tv show, which has a near 100% success rate. That's the way profilers want to be seen, but it doesn't work out like that. So if you have numbers, preferably in percentages rather than total successes with no context, that would be a good start.
While I agree, CI doesn't have a 100% rate, but yeah a pretty darned unbelievable rate of like 99% or something. (They let one get away every now and again.)
Chikatilo the subject of a movie back then (Score:2)
Was this the one protrayed by Malcolm McDowell? I don't know if anyone here has seen that... I think he was the only recognizable one in that film.
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Do you mean Citizen X [imdb.com] which starred Stephen Rea, Donald Sutherland, Max von Sydow?
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Turns out mine is more recent, Evilenko http://www.imdb.com/title/tt0406754/ [imdb.com]
Just the data, ma'am, please.. (Score:5, Insightful)
Oh man, I get so bothered when someone presents interesting data - only to append a theory that isn't connected to it.
Why is that? Don't you get to publish unless you have a theory, no matter how unrelated an implausible it is?
Human sciences especially - it's understandable though, as it's hard to read people's minds.
Neurons firing? Really?? Does fantasizing about objects we can actually see and touch suddenly make it science?
If the study included brains scans or something, sure. But all they did was look at numbers.
If you don't have a theory that's related to your study, just post your data and spare us your fantasies. Thank you.
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If you don't have a theory that's related to your study, just post your data and spare us your fantasies.
Posting datasets and the theories that do NOT fit is also valid... though the publication should note that it's main purpose is to get the data out there and show that some work was done to "figure out" the data but no conclusions were drawn.
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It would be great if you kept to one point on a rant. Generally, adding a theory does bother me, because in a lot of cases it seems very convoluted, and in many cases does not even follow from the data presented.
You also seemed to attack the premise of neurons firing, suggesting it lacked credibility. I think this makes sense, in the same way as someone who takes anti-psychotic medication, then skips it for a while. In this case, killing takes the place of the medication, sating whatever imbalances or pr
The Sudoku Killer (Score:5, Funny)
And in other news, police warn that the Sudoku killer will kill either 1, 4, or 9 victims next.
Power-Law distributions in empirical data (Score:4, Informative)
Here is the abstract of an article, "Power-Law distributions in empirical data" by Clauset et al (2009):
"Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events— and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a powerlaw distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out."
So, I would recheck this guy's analysis.
That seems backwards (Score:2)
Given any dataset, you can come up with a formula that would match it.
That doesn't mean though that if they tried doing this back when he was on his 3rd or even 20th murder, they'd have managed to come up with something useful.
North Korea (Score:3)
1 guy (Score:4)
You don't build a statistical model off of a single person.
Psychopaths (Score:3)
I don't know if Chikatilo was a psychopath, anyhow, psychopaths seem to enjoy hurting others and are usually pretty smart. There is a secure institution where a buch of psychopaths managed to get hold of the manual for a well known profiling instrument that, effectively scored psychopathology from 0 to 40. They then had t-shirts printed with just "Perfect 40" on them. Point being that once something is public knowledge the kinds of people who engage in this kind of activity are likely to pay attention and work to throw predictive algorithms off, simply because they would gain a great deal of satisfation doing so.
How Many Deaths for a Sufficient Data Set? (Score:4)
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Well, isn't any number less than the number he would have killed had he been allowed to die of natural causes, by definition, an improvement?
The tool is what it is, if it is anything, of course. Leaving aside whether this may actually be meaningfull, the attempt here is to figure out how to apportion resources towards actually catching a serial killer. You have to consider it in that context. These crimes are happening, and will continue to happen, whether anything is done or not. There are limits to the re
Citizen X (Score:2)
this too is profiling... (Score:4)
Sorry, but, hand-waving at neurons to justify the power law they found is none the less also....
"relying on the junk science of behavioral profiling"
Re:Yeah I saw that on... (Score:5, Insightful)
Numb3rs already. Yawn.
Dear teeloo,
Many of us reside outside the US and/or have lives.
Sincerely,
The rest of /.
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Many of us have torrents and like Us crime dramas without ads.:) (probably)
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Many of us have torrents and like Us crime dramas without ads.:) (probably)
dumbers hardly fits into that category
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How would one know? It gets through the mental pipeline as far as filter #2 (made in America) and at that point I move onto the next programme for consideration.
A crude filtering system I'm sure ; but it cuts the amount of TV to be actively considered for watching down to a mere couple of dozen hours per night, which is manageable at 15 seconds consideration per hour broadcasting slot.
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There is no laugh track. They just film in front of a studio audience.
You don't find it funny, which is fine. Clearly the people in the audience do - which is also fine.
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Many of us have better taste in TV.
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Many of us have torrents and like Us crime dramas without ads.:) (probably)
Buy Sky+ then. Oh, sorry, I forgot this is slashdot so we're entitled to anything we can get our hands on and believe that films and TV shows magically get made at no cost.
Yeah, blah blah "Intellectual property" doesn't really exist, it's only copying not stealing, whatever.
Re:Yeah I saw that on... (Score:5, Interesting)
Unfortunate that you got modded troll, because you make a good point.
I have to ask, though - At what point do you consider time and/or format shifting as "piracy", for ethical purposes?
If I watch live TV, no piracy, ostensibly because we see the ads that "pay" for it. But I can (and back before TiVo, most people did) use commercials as food/bathroom breaks, or just flip channels during them, so even in the bad-ol'-days, no one really watched them.
If I buy the season on DVD, no piracy, because I've actually directly paid for the content.
If I download the same show from a torrent, most of us would agree that violates the spirit of copyright, even if we don't particularly care and do it anyway.
If I rent the DVD and rip it, I think most would consider that piracy.
And of course, we have the DVR, where I can time and format shift it to watch wherever and whenever I want, which IMO most people have come to accept as not piracy.
But - How does ripping or torrenting differ from the DVR case, either functionally or in terms of compensation? Whether I "rip" a show from broadcast TV or rip it from a DVD, it makes absolutely no difference to the producer. Whether I download it from a torrent or "download" it from my TiVo To Go, it makes absolutely no difference to the producer. Whether I watch it live and promise to completely ignore the commercials, or watch a torrented 4th-hand fansubbed unlocked-PSP version, it makes absolutely no difference to the producer.
Basically, once the producer has "given it away" by broadcasting it to the world, how can any use of that content really fall into the same box as "stealing"?
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This is more a statement of the apparent ineffectiveness of advertising. The fact is that the majority of advertising is largely ignored, but they are simply looking for brief impressions that yield small returns, but are also very cheap per impression. If you are skipping it with your DVR, you'll probably still catch the beginning and end of each commercial break and at least have a small impression. For marketers, even that small impression being mixed in is still worth paying for. Maybe you aren't se
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For no other reason than that the government says it does ...
This is the problem with copyright (and Patents) they make no sense with modern technology, either you ban what everyone would agree is normal legal use, or all copying is valid and legal ...
It's like putting a film on a huge screen in a public place then trying to sell ticket to people to watch it ... ?
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In the DVR example you've taken advantage of a specially licensed showing of the copyrighted content. Whether you watch the commercials or not is just part of the formula they use to calculate the rates for that show.
So saying that using a DVR is indistinguishable from downloading a torrent copy is like saying because Costco is giving out free cheese dip samples today, you have the right to eat free cheese dip for life.
A certain percentage of tasters will buy the cheese dip, others will simply go to Costco
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I'd like to see someone (other than me) test this by downloading a show while it is being shown on over-the-air TV, as a rerun. They were giving it away free at that time, the lawyer argues, and my client has an antenna with HD reception. How do you ensure the audience stays in their seats for the commercials? Keeps their eyes open? You don't? I move for immediate dismissal.
Terabytes of Tivo To Go content (Score:2)
So I have had half a dozen Tivos, lots of them have been networked on my home LAN. I have several 2 Tb drives on my home machine, after Tivo Desktop pulls the shows, I have VideoRedo automatically mark the commercials, cut them and then dump another file in MPEG format sans commercials for long term archiving.
Content Producers get paid by networks, networks get paid by advertisers. I pay Comcast a large sum of money every month for content, they in turn pay networks for access to that content. The Content P
format/time shifting is piracy, not fair use... (Score:2)
Really? you don't see the difference? assuming you aren't a troll, what are you not getting? When you get content from your Tivo -- like say, a season of Numb3rs from Netflix, to kinda stay on topic -- the studios were compensated by Netflix. fwiw, Netflix paid over US $2B in licensing fees for the content they provided in 2011, and they will be paying 10X that amount in 2012. In contrast, the studios received zero compensation from the thief that provided you a torrent of that same season of Numb3rs.
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Numb3rs already. Yawn.
Dear teeloo,
Many of us reside outside the US and/or have lives.
Sincerely,
The rest of /.
Uh, no, the rest of /. knows how to use a search engine.
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And, of course, the thing to remember about Numb3rs is they didn't really have a genius mathematician who solved all of these problems. Much of the math was solid-sounding, but generally they weren't afraid to use math like Star Trek used tachyons and just make stuff up.
So, the fact that real statisticians identified this is in no way lessened by anything you saw in Numb3rs.
Also, Superman doesn't really live in New York City, and Jack Bauer isn't a real guy. Oh, and there is no Santa
Re:Yeah I saw that on... (Score:5, Informative)
Also, Superman doesn't really live in New York City,
We know that. He lives in Metropolis. Duh.
Re:Sounds like the dude... (Score:5, Funny)
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Suddenly Senior High doesn't sound like such a safe place...
Re:Sounds like the dude... (Score:5, Funny)
Sleeping with serial killers saves lives!
... but not necessarily yours...
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I know you're trying for the funny but a lot of them are married or have girlfriends.
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True, but from what I've read about the topic (hey, serial killers are fascinating in their own morbid way) there are also plenty of them that seem to have turned to true crazy after spending many years as unwilling social outcasts.
So to a small degree the parent poster may be sort of right, there might now somewhere out there be some guy who just happened to finally get laid and thanks to that he never snapped completely...
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So to a small degree the parent poster may be sort of right, there might now somewhere out there be some guy who just happened to finally get laid and thanks to that he never snapped completely...
As I would assume everyone on slashdot knows, you can get broadly the same physical release from masturbation as actually having sex. The profound psychological issues associated with being a serial killer won't suddenly vanish just because you get to come inside a woman instead of a tissue.
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Of course that connection can be good or bad, or even indifferent but it's still a connection.
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Thats what I was thinking, sex is more than just physical, it's also about a connection with another living being. Of course that connection can be good or bad, or even indifferent but it's still a connection.
huh? I don't feel any "connection" with the woman servicing my johnson, anymore than I feel a connection with the mechanic servicing my Ducati. Sex is friction, dude, anything else is pretty much just emotional baggage. It's a transaction, certainly, and it can even be a two way transaction, if the woman can let go of the emotional baggage and focus on the sex. Or are you female? (Unlikely in this forum, but possible.) If you are female, then yes, you (probably) think you need some kind of emotional at
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Despite what the commercials say, your body knows the difference between sugar and corn syrup.
There's a reason why we have a sex drive. It fills an important reproductive function. Humans and other animals are full of all kinds of bits and pieces driving us to perform our reproductive functions. Orgasm is a neat little reward feedback mechanism, but it's far from the only part of the human sex drive. It's made up of all kinds of bits, some of them pure genetic programming, some shaped by environment. Someti
Re:Sounds like the dude... (Score:5, Insightful)
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Re:Sounds like the dude... (Score:5, Funny)
And since the keyboard is mightier than the sword beware. I have a keyboard and I'm not afraid to use it.
You own an IBM Model M keyboard?
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And since the keyboard is mightier than the sword beware. I have a keyboard and I'm not afraid to use it.
You own an IBM Model M keyboard?
A Model M is dangerous only if you have better upper body strength than the typical slashdotter.
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A Model M is dangerous only if you have better upper body strength than the typical slashdotter.
Mine is balanced above the door. A type of trap.
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Re:Sounds like the dude... (Score:5, Funny)
Some men are driven to drink, use drugs, post on slashdot in such situations. Others may be driven to commit homicide.
Some write Byzantine filesystems. Some do both.
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I know you're trying for the funny but a lot of them are married or have girlfriends.
Actually, the getting laid thing is mostly bollocks. Many serial killers have trouble either forming, or maintaining a normal sexual relationship with women.
If we look at most serial killers such as Berkowitz or Gacy, they had serious sexual deviancies. Gacy was married too, yet was still deviant (he was a Peado)
Re:Sounds like the dude... (Score:5, Interesting)
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> even had women fawning over him AFTER they had learned he was a serial killer
That's not an indication of charm, as the "there's no bad publicity" goes, it 's quite likely that some guys have more success with woman after it is revealed that they are serial killers..
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Lack of knowledge about the killer's neural activity is what he has in common with the researchers. So hush, we're doing science here. Science in the dark.
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Tell that to Jack the Ripper.
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murdered less frequently? (Score:2)
Is there an acceptable frequency for murder? Does it grow more acceptable as its frequency is lower?
Sometimes, some mathematicians scare me.
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I wonder how they got their hands on the brain activity data of a serial killer in action?
They didn't. They "assume" it may be the same as epilepsy based on a 1879 (yes, 1879) book by a criminologist called Lombroso who believe that crime was caused by hereditary defects or the 'reversed' evolution of some populations. While discredited by later work, it remained a favourite source for people who wanted reasons to believe certain populations were inherently criminal or defective, in order to justify exterminating or sterilising them (along with the disabled).
However, Lombroso [5] long ago pointed out a link between epilepsy and criminality. A link between epilepsy and psychosis had been also established [6]. Thus, one may speculate that similar processes in the brain may lead to both epileptic seizures and serial killings.
While I am not a very 'politically co
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great points. thank you for posting this; it saved me some time.
although identifying "power law" with "my pet theory" is the worst of their sins (there are many reasons to have a power law), their technical methods are poor as well. i recommend [http://cscs.umich.edu/~crshalizi/weblog/491.html] for an accessible read about how obvious and accepted methods break down when dealing with power laws.
i was going to say that he was a young person desperate for publications (the more sensational the better), but lo