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Serial killer's behavior explained with mathematics

Serial killer's behavior explained with mathematics

Posting in Science

Scientists have found a curious similarity between a serial killer's murders and the firing patterns of brain cells.

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

Contributing Writer

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. Disclosure