A simple mathematical model of the brain explains the pattern of murders by a serial killer, say researchers
On 20 November 1990, Andrei Chikatilo was arrested in Rostov, a
Russian state bordering Ukraine. After nine days in custody,
Chikatilo confessed to the murder of 36 girls, boys and women over a 12-year period. He later admitted to 20 murders, making him one
of the most prolific serial killers in modern history.
Today, Mikhail Simkin and Vwani Roychowdhury at the University of
California, Los Angeles, release a mathematical analysis of Chikatilo's
pattern of behaviour. They say the behaviour is well characterised by a
power law and that this is exactly what would be expected if Chikatilo's
behaviour is caused by a certain pattern of neuronal firing in the
brain.
Their thinking is based on the fundamental behaviour of neurons. When
a neuron fires, it cannot fire again until it has recharged, a time
known as the refractory period.
Each neuron is connected to thousands of others. Some of these will
also be ready to fire and so can be triggered by the first neuron. These, in turn, will be connected to more neurons and so on. So it's easy to
see how a chain reaction of firings can sweep through the brain if
conditions are ripe.
But this by itself cannot explain a serial killer's behaviour. "We
cannot expect that the killer commits murder right at the moment when
neural excitation reaches a certain threshold. He needs time to plan and
prepare for his crime," say Simkin and Roychowdhury.
Instead, they suggest that a serial killer only commits murder after
the threshold has been exceeded for a certain time.
They also assume that the murderer sedates the killer,
causing the neuronal activity to drop below the threshold.
Simkin and Roychowdhury used their model to simulate the pattern of
firing in a brain to see how often it surpasses a given threshold long
enough for a murder to take place.
In the model, they used a 2 millisecond period as the fundamental
time step, that's about the time between firings in a real neuron. And
they simulated some 100 billion time steps, equivalent to 12 years or
so, that's about the period 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.
That's a well known property of power law distributions that holds
true for all kinds of phenomenon. A large earthquake, for example, is
more likely soon after another large earthquake.
Interestingly, Simkin and Roychowdhury's work bares much similarity
to other recent work suggesting that the distribution of epileptic fits
also follows a power law. The reasoning here is the same too--that
patterns of neuronal firing can spread through the brain, like an
avalanche, causing a fit in the process.
This suggests an obvious avenue for future research in working out
whether other forms of extreme behaviour, and indeed ordinary behaviour,
follow the same pattern. Perhaps these guys and others are already
working on the data.
Chikatilo was eventually convicted of 52 murders and executed by a gunshot to head in 1994.
Ref: arxiv.org/abs/1201.2458: Stochastic Modeling Of A Serial Killer
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