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Serial killer’s behavior explained with mathematics

By | January 17, 2012, 6:31 AM PST

Andrei Chikatilo is a Ukrainian-born serial killer, aka The Butcher of Rostov, who confessed to murdering 56 children and women, between 1978 and 1990. Now scientists have performed a study that suggests his killing pattern matches a typical firing pattern of brain cells. (What will scientists study next?)

Neurons in the brain fire and it’s this firing that ultimately leads to our thoughts, actions, emotions, in fact everything we do. When a neuron fires it launches a domino effect among surrounding neurons that sets into motion a sort of avalanche of firing action. This is how the brain works. Waves of sparks, as it were. But here is a key point: After a single neuron fires it cannot fire again until it re-charges. This is known as the refractory period.

The two scientists, Mikhail Simkin and Vwani Roychowdhury at the University of California, Los Angeles, have found through mathematical analysis a connection between Chikatilo’s pattern of killings and the firing pattern of neurons.

From the TechReview post:

…they suggest that a serial killer only commits murder after the threshold [of neuronal firing] has been exceeded for a certain period of time. They also assume that the murder has a sedative effect on the killer, causing the neuronal activity to drop below the threshold.

Simkin and Roychowdhury simulated about 100 billion time steps of neuronal firing, roughly equivalent to 12 years (the length of time that Chikatilo was active.)

The results are remarkably similar to the distribution of Chikatilo’s real murders and Simkin and Roychowdhury speculate that it would be relatively straightforward to introduce a realistic correction factor that would make the fit closer.

They say: “One could enhance the model by introducing a murder success rate. That is with certain probability everything goes well for the killer and he is able to commit the murder as he planned. If not, he repeats his attempt the next day. And so on.

This model leads to an interesting insight into the nature of serial killing. It suggests that the likelihood of another killing is much higher soon after a murder than it is after a long period has passed.

Meaning, there is a sort of momentum component that is often found in other physical and biological events. The key thing is here is a mathematical pattern called a power law distribution. A power law describes a mathematical relationship between two things. When the frequency of an event varies as a function of some variable of that event, like its size for example, the frequency of the event follows a power law. For instance, the “long tail graph” made famous by Wired editor Chris Anderson is a power law graph:

This particular power law graph is also known as the Pareto principle, or the 80-20 rule, where for many events 80 percent of the output comes from only 20 percent of the cause, or input. Power law distributions can be found in many events, biological and physical. From the behavior of large earthquakes, to solar flares, to the frequency of words in a language.

Worth noting is that the Occupy Wall Street protesters are, at least according to their slogan of “We Are The 99%”, protesting Pareto’s principle which is found in business, science, economics and as noted above, in natural systems. Unfortunately it is not something within our control. Complex systems, for better or worse, tend to develop a concentration of extremes. The breadth of areas where we find such a consistent pattern is what is truly amazing.

And now, according to these researchers, Pareto’s principle can help explain the behavior of a serial killer. There have also been studies that suggest epileptic fits also follow a power law, meaning that the patterns of neuronal firing can spread through the brain and cause a fit. It may be the case that we’ll find a lot of more of our behaviors follow a power law distribution.

[via Technology Review]

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Christie Nicholson

About Christie Nicholson

Christie Nicholson is a contributing editor for SmartPlanet.

Christie Nicholson

Christie Nicholson

Contributing Editor

Christie Nicholson produces and hosts Scientific American's podcasts 60-Second Mind and 60-Second Science and is an on-air contributor for Slate, Babelgum, Scientific American, Discovery Channel and Science Channel. She has spoken at MIT/Stanford VLAB, SXSW Interactive, the National Science Foundation, the National Research Council, the Space Studies Board and Brookhaven National Laboratory. She holds degrees from the Columbia University Graduate School of Journalism and Dalhousie University in Canada. She is based in New York.

Follow her on Twitter.

Christie Nicholson

Christie Nicholson

Christie Nicholson does not hold any investments in the technology companies she covers.

She writes for SmartPlanet and is not an employee of CBS.

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0 Votes
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You put the cart before the horse
Neurons do not "fire" and then we have thoughts. We have thoughts and then neurons "fire". This is not the first time scientists have been able to model some behavior mathmatically. This same law of distributions could apply to the race car driver, one night stander, or any of a myriad things that result in a rush of adrenaline and other neurotransmitters. This guy some how latched onto murder as his high of choice. The problem will be that if this particular link is made then anytime scientists can show this particular neural activity pattern then the association that the person is a serial killer.
Posted by randall.wilkinson@...
17th Jan 2012
0 Votes
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bumps on the head
Yeah, and Phrenology was once considered real too!
Posted by tech_ed@...
17th Jan 2012
0 Votes
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It's only a matter of time...
Ok... So now it's only a matter of time until some lawyer uses this as a defense in a murder case. "My client was the innocent victim of misfiring neurons."

Wait for it... wait for it...
Posted by coolblueice
17th Jan 2012
0 Votes
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Replace jails with mental hospitals!
It seems that a reasonable argument can be made for the hypothesis that all violent behavior is caused by misfiring neurons (and hence is ultimately a mental illness). This does not mean we let the individuals who have these illnesses off scot-free. They need to be locked up along with the vaccine refusers because their disease can kill others if left untreated. People should not have a choice about being treated for psychopathy. If there is no known cure for a particular from of psychopathology, the people presenting it need to be locked up until they are dead or a cure is found. A "cure" needs to be verified and if a psychiatrist believes someone is cured, they need to have some skin in the game if it turns out the cure was a fake. Maybe we need the psychiatrist to put up a bond which would leave him liable to lose his house if it turns out he guessed wrong and one of his patients kills again.
Posted by uftr@...
19th Jan 2012
0 Votes
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Fitting the curve
I wonder how long it took to find a mathematical relationship that the data would fit?

1) Define the data points
2) Run the software to find the curve
3) Publicise the curve

It really sounds like a "Publish or lose tenure" situation. You get into the soft sciences and they can play some real games with data. I remember seeing a Biology (borderline hard/soft science) paper where an R factor of 0.3 was considered good. I'm a chemist. If I got results like that I'd service my measuring device.
Posted by metaphysician
18th Jan 2012
0 Votes
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Thinking leads to murder?
So, You have to be able to think in order to commit a murder? Who would have thunk it? No wonder there are so few murderstories about evil walls or spoons.
Posted by Dukhalion
23rd Jan 2012
0 Votes
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Inanimate killers?
Yep, who'd have thunk it?! Multiple murderers make a decision to murder.
Following the political responces in several countries though you would think that there is a link between inanimate objects and the deed. Let me think though...
I never heard of a murderer saying, "...the voices in my hammer told me to kill people". Or have you heard the phrase, "the knife made me do it!" Probably not.
While some people poo poo this sort of research I think society has to look at ways of coping with prolific killers. Possibly predicting their behaviour once they become active makes sense. Legislating against possible implements they might choose, or reactively increasing security is not the smart way to deal with this problem. [BTW I'm not advocating ignoring security.]
Of course there's also the other thing to consider. Empowering people to defend themselves; this is taken for granted in the US but people don't get the same support in other countries.
Posted by Porrett
25th Apr 2012
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Pareto principle
Your offhand throwing in of the 99% slogan of the occupy movement is off base.

If 20% of people controlled 80% of wealth, that would be a stable, or normal situation. The problem now and either a symptom of or cause of instability is the fact that 80% of the overal wealth is controlled by a much smaller group than 20%.

Every time such a disparity has occured historically, a correction (or war or revolution) has occured.
Posted by dimonic
24th Jan 2012
0 Votes
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The pareto law applies to optimum functioning of the economy
The problem being that if the distribution of wealth to owners reaches or exceeds a parato distribution, the economy fails to function optimally. It also doesn't function optimally at a totally level(1 to 1) distribution of wealth to owners. The optimum being a small dynamic range lying between those two extremes.

Unfortunately, the majority of economists and financial experts are too stupid (i.e. unable to be trained out of it) to understand this concept and usually adhere to the fallacy of unlimited markets.
Posted by Dr_Zinj
24th Jan 2012
0 Votes
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Murder by Numbers
This was discussed in a song a while back, "Murder by Numbers" by the Police.
Posted by jkmartinez2@...
24th Jan 2012
0 Votes
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Serial Killer's Behavior
So unlike labor pains and menstrual cramps for women, this really IS all in his head.
Posted by jayohem@...
24th Jan 2012
0 Votes
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Not fascinating
Usually I find scientific analysis very intriguing but in this case I find it revulsive. I cannot sit and read this objectively and think that "well that explains that" as I can with most things. In the case of serial killing I don't care how their brain is malfunctioning, they should be stopped and if need be eliminated as they are a broken part of the biological model and not fit for study. Will knowing this allow science to stop this kind of behavior? doubt it. Who would you screen? I can only carry detached analysis so far. This is sick
Posted by sbentjies
24th Jan 2012
0 Votes
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Not very interesting
So the scientists have found that serial killing is somehow associated with becoming agitated. Well that's quite a revelation. I guess we can rule out that they did it in their sleep. We still don't know if the relationship is causal. We can't say whether the agitation caused the killing or the anticipation of the deed caused the agitation. Perhaps there is a lurking common cause. So much we don't know and this article sheds very little light.
Posted by john.ballantyne@...
24th Jan 2012
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Pareto's Law and Occupy Wallstreet
Christie when you assert that "Worth noting is that the Occupy Wall Street protesters are, at least according to their slogan of We Are The 99%, protesting Paretos principle which is found in business, science, economics and as noted above, in natural systems. Unfortunately it is not something within our control." you are seriously missing the concept.

Yes, income distribution is likely to follow some sort of power law. Nobody is challenging that. The question is entirely about the differences in the parameters of the equation.

You hopefully realize that if your mortgage rates went up to 25% a year, you would be dealing with the same amortization equations, just a different paramenter - but that difference can matter a lot.

Income and wealth distributions in the 1950's still followed a power law, but the curve was much less steep - the top 1% earned and owned a smaller portion of the total than today; and every decade this curve gets steeper under current human laws. And yes we very definitely can and do change that - the steepness of the curve has gone back and forth several times in the last century, depending on things like taxation rates and degree of special treatment for capital gains. It got steeper in the 30's, shallower in the 40's and 50's, and steeper again since then.

The magnificant palaces of the kings and starvation of peasants was also following a power law - just different parameters. That changed.

The current movement of wealth towards the top is specifically due to human changes in laws and taxation rates which began to favor the wealthy more than they had in the 50's; those laws and regulations could change again without violating any natural laws.

This is a factual analysis, entirely separate from the question of whether we should have laws and regulations which favor movement of wealth towards the top or which favor relatively shallower curves - people can argue for either case logically (tho most just regurgitate political stances rather than objective analyses). I'm not arguing that here. I'm just taking issue with your misunderstanding that the current very steep and increasing power curve of income and wealth in the US is some kind of natural law that one would be naive not to accept. The general curve is inevitable, but the steepness of it is entirely dependent on human laws and regulations. The Occupy movement seeks to change the steepness of that curve - a goal we can endorse or oppose, but on other grounds than "natural laws".
Posted by zhahai
Updated - 2nd Feb 2012
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