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(Male announcer) Thank you for downloading from the BBC.

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For details of our complete range of podcasts and our Terms of Use,

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go to bbcworldservice.com/podcasts .

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(Female announcer) Governments worldwide battle to control and contain terrorism.

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Police and the courts struggle to separate harmless loners from dangerous lone wolves.

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Opinions differ on the most effective way to combat terrorist attacks,

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from military interventions on the ground, to curbing political and religious radicalisation.

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But in this edition of Discovery, we'll be hearing about a more unusual new weapon

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that might be used in the future to fight terrorism:

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maths (1:00)

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(A) We were looking at the data in a new way, we were
using tools that were somewhat foreign,

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(A) these were tools that came out of physics
and complex systems, not tools that necessarily came out of the political science community.

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(A) And we were saying things that were kind of weird.

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(B) One thinks of terrorism as something very random, 
something so strange that it must be done in a very
chaotic way.

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(B) But of course, in the end, it is an activity, it's a
human activity, so it's quite interesting then that the
patterns that you seen in the events are not random.

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(A) For terrorism, that had somewhat shocking implications.

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(A)If you understand the frequencies of the small 
events, you can extrapolate,

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(A) and then make a forecast out into the future, 
about what the probability should be

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(A) for a very large event.

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(HF) So, could maths predict the next 9/11?

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(HF) You're listening to the BBC World Service, and today
on Discovery, I'll be looking at the hidden mathematical
pattern that is being discovered in global terrorism;

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(HF) a pattern that lies behind a host of diverse phenomena,
from economics to earthquakes.

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(HF) I'm Dr Hannah Fry, and I'm a mathematician from
University College London, working on complex systems.

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(HF) These are systems, like terrorism, which at first seem
complex, and random

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(HF) but if you stand back and study the bigger picture, then
a surprising number of patterns can appear;

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(HF) patterns which you can describe using mathematics.

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(HF) Dr (?), a computer scientist at the University of
Colorado, was one of the first to find a tangible,
mathematical connection underlying terrorism.

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(HF) He looked at 30,000 terror attacks worldwide, over
40 years

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(HF) and for all of the events, he counted how many times a
certain number of people were killed, and plotted it on a graph


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(HF) and the results were remarkable.

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(Dr) This initial analysis we did, it was quite shocking,
we found this thing that looked like

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(Dr) what's called a power law distribution, which is a 
very special kind of mathematical pattern that usually

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(Dr) crops up in physics, in fact, but increasingly is 
observed in social and biological systems,

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(Dr) and this is somewhat surprising, because when we 
think about terrorism,

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(Dr) we think mainly about the capricious, highly 
contextualised nature of the individual actors

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(Dr) that carry out these events,

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(Dr) and yet, at the global level, we see this remarkable
pattern, this power law pattern, emerge.

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(HF) So it's obviously a bit tricky to describe a graph
on the radio. (Dr) [Laughs] Yes.

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(HF) but could you give us an idea of what a power law
looks like,

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(HF) perhaps, compared to some other distributions that
people might be familiar with?

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(Dr) So a power law distribution is very different from


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(Dr) what most of us experience, and our intuition 
is built around, as human beings.

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(Dr) Most of our world is wrapped up in what are called
Gaussian, or normal, distributions.

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(Dr) So, the range of heights that we experience
among other humans,

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(Dr) has what's called a normal distribution.
(HF) Like a bell curve.

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(Dr) [Confirming] Like a bell curve. Which means that
there's an average,

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(Dr) that is representative of essentially the entire population.

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(NJ) One of the first graphs that we ever draw in
school is one of heights of people in the classroom.

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(HF) Neil Johnson, professor of Physics at the
University of Miami.

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(NJ) There's usually some great big peak, and there's a
little bit of spreading either side of the peak,

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(NJ) Might be something like, you know, for adults,
5 foot 6 or something like this,

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(NJ) that's the average, and of course people have wide
variation; basketball players, and there's also

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(NJ) people who are much shorter, but nobody's a foot
tall in the adult population, and nobody's 20 feet tall.

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(NJ) Well, that's not how it works for the severity of
attacks.

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(NJ) You might <i>think</i> it would have, you know, in an
attack, people use an explosive device.

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(NJ) You might <i>think</i> it blows up a typical number of
people, you know, plus or minus 3.

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(NJ) But no, it's a completely different distribution.

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(NJ) It is the equivalent of having the 20 foot person,
and the 1 foot person happening pretty frequently.

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(HF) A power law curve looks like the downward slope
of a hill.

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(HF) At the top left, you have a large number of small
attacks that kill a few people,

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(HF) and at the bottom right, you have a tiny number of events that are very severe,

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(HF) with hundreds, or thousands of deaths.

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(HF) Behind this graph lies a very simple equation,
providing a clear mathematical link

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(HF) between smalll, frequent attacks, and rare,
large-scale strikes.

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(HF) Now this shape has been found time and time
again, over different decades, in different cities,

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(HF) and for different terrorist groups.

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(HF) And despite huge changes in global geopolitics,

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(HF) from the fall of the Soviet Union to the rise of
Islamic extremism,

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(HF) this simple mathematical pattern has persisted.

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(Dr) The remarkable thing about the power law
distribution in the sizes of terrorist events,

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(Dr) is that it seems to be very robust, so it suggests that
this may be a fundamental pattern,

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(Dr) it may be that the nature of the modern world
produces this pattern,

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(Dr) so from a policy perspective, there is an
implication that changing this pattern,

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(Dr) being able to reduce the likelihood of a large
terrorist even like 9/11 happening again

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(Dr) may be not as simple as finding the terrorists and
throwing them in jail.

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(Dr) It may be more subtle, it may be that the nature of
the global system

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(Dr) tends to produce the types of individuals that would then go about carrying out

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(Dr) these kinds of events.

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(Dr) And that's a much harder problem to solve from
a policy perspective.

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(HF) So how easy was it for you to get your work
published on this?

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(Dr) (laughs)
(HF) (laughs)

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(Dr) I'm laughing because it was not easy.
(HF) Yeah.

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(Dr) My colleague, Maxwell, and I started this work in
2003, when the Iraq invasion

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(Dr) was really getting going,

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(Dr) and the paper was not published until 2007.

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(Dr) There were many factors that made it difficult, but
I think one of them was that this was

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(Dr) such a weird take on a problem that people had
been thinking about for a long time.

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(Dr) Political scientists have been studying terrorism for
decades,

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(Dr) so we were looking at the data in a new way,

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(Dr) we were talking about terrorism not as a
phenomenon of decision making,

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(Dr) but almost as a natural phenomenon.

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(Dr) This idea that we could look at the entire world
almost as a natural kind of system,

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(Dr) and characterise its patterns without having to refer
to the actual decisions that produced the events.

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(Dr) So the unpleasant aspect of trying to get this
work published is that we tried 10 different journals

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(HF) Wow.
(Dr) in order to get this published,

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(Dr) and sometimes the reviews we got back from
academics, they seemed to be

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(Dr) missing the point, in some ways.

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(Dr) They didn't understand what we were doing,
or what the results implied.

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(HF) So I understand one of the really important
implications is about really large events.

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(HF) What did you find there?

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(Dr) The fact that the power law pattern exists,

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(Dr) and the implication that these are all part of
the same fundamental process,

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(Dr) it does imply that the largest events, things like 9/11,

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(Dr) will occur with surprising frequency, and the
mathematical function is strong enough

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(Dr) that one can actually extrapolate, and then make a
forecast in much the same way

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(Dr) that forecasts are made for earthquakes.

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(Dr) In fact, the power law distribution is the same
distribution

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(Dr) that characterises the frequency of earthquakes,
and the frequency of terrorist events.

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(Dr) The shape of the distribution is slightly different,
but the pattern is the same.

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(Dr) And so, by applying this mathematical model to
forecasting, we can make an estimate

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(Dr) of the probability that we should see an event in the
next 10 years, for instance,

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(Dr) that kills as many, or more people as 9/11 did.

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(HF) And what did you find?

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(Dr) The likelihood across the set of models that we
fitted to the data, over the next 10 years,

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(Dr) is somewhere around 30%, which is not a 
certainty,

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(Dr) but it's still an uncomfortably high number.

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(N1) At least a hundred people are reported killed, and
five hundred injured

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(N1) in a chain of car bomb attacks across Bombay.

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(HF) In 1993, 13 bombs exploded within 3 hours in
Bombay, and at the final count, over 1500 people

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(HF) were killed or injured.

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(N2) Russia observes two days of national mourning
for the many victims of Beslan.

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(N2) More than 100 funerals take place in one day,
attended by thousands of people.

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(HF) The Beslan school siege in 2004, carried out by
Chechen rebels,

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(HF) hit over 1000 children, parents, and teachers.

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(HF) And, after 9/11 - the largest terrorist attack in
human history, which killed almost 3000 people -

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(HF) funding was ploughed into new, scientific ways
to try and tackle terrorism,

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(HF) from using Game Theory in airport security
to analysing the social networks of terror suspects.

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(HF) But now, researchers are using data on terrorism
in insurgencies to try and forecast future attacks.

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(HF) Physicist, Neil Johnson, from the University of
Miami, studied the timings between

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(HF) terrorist events in one area, and, strangely enough,

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(HF )the same kind of power law pattern lay behind this data too.

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(NJ) Our initial study was looking at a few regions in
Afghanistan, and Iraq.

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(NJ) We've now done the study across basically every
country where we could find data -

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(NJ) that includes Africa, includes suicide bombings
of Hezbollah

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(NJ) we've looked at suicide attacks in Pakistan,

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(NJ) they all seem to follow this relationship.

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(HF) So if this happened then, for example, in a UK
city, how confident could you be

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(HF) in predicting the timing of the next attack.

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(NJ) Yeah, of course it will never be down to the day;

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(NJ) it will be, in some situa- like, you know- if it's down
to the week.

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(NJ) But what can be very useful is predicting the trend.

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(NJ) Are we going to see the events get less
frequent in time?

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(NJ) Are we going to see them get more frequent?

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(NJ) And if we see them get more frequent, roughly
how many are we going to be getting

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(NJ) every few weeks?

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(NJ) It's not meant to be like predicting, you know
whether it's going to rain in the next three days,

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(NJ) it's meant to be some trend, and I very much see it
in that analogy with say, weather prediction.

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(NJ) The medium-term weather forecasts are getting
better and better,

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(NJ) but it's still very hard to say that at 5 o' clock,
in three days,

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(NJ) rain will fall on a particular place in London.

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(NJ) But we're all very interested, and very keen, to
know when some front is moving through,

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(NJ) and over the next three days, there'll be some
increase in the trend of rain.

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(NJ) That is a very useful statement.

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(NJ) And it's exactly that level [of] prediction that we
believe that this type of work is good for.

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(NJ) It's never going to say that in five days' time,
[in] a particular place, there'll be a particular attack,

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(NJ) but what it is saying is: wait a minute, <i>this</i> group,
in <i>this</i> region of a country,

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(NJ) <i>they</i> are escalating.

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(HF) So I suppose it goes without saying then, that
these ideas would be incredibly useful

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(HF) to counter-terrorism agencies, but how much
interest have they shown in your research?

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(NJ) Well, I'm currently funded by the Office of Naval
Research,

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(NJ) they've been very supportive, they're very
interested in this.

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(NJ) I've also had funding through another agency
which was interested in counter-IED strategies.

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(NJ) So I would say that there's been a lot of interest,

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(NJ) and we've even had interest, I remember getting
an email from Marines

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(NJ) in a forward-operating base in Afghanistan, telling
me that they'd been trying -

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(NJ) because the formula is so simple, the mathematics
is actually so simple -

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(NJ) that they'd been trying out this particular analysis
of successive events that

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(NJ) they'd actually been seeing, and experiencing
around them.

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(HF) Wow. So Marines in the field have been in contact
with you, talking about your mathematical models, then?

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(NJ) Yeah, the intelligence officer from one of the
units, yes.

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(HF) But not everyone is convinced that we can make
such precise predictions.

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(HF) Dr Karsten Donnay is a social scientist from
the Swiss Federal Institute of Technology,

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(HF) who specialises in conflict modelling and
simulation.

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(HF) He thinks there's a danger that these models can
be taken too far.

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(KD) I think one has to be very careful about using
this for direct prediction,

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(KD) I mean we do distinguish between a prediction
and forecasting.

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(KD) If you talk about long-term predictions, then it's
feasible to make statements like this:

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(KD) There's (??) this chance that in the next 10 years, an event of a certain size will occur,

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(KD) that's definitely possible.

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(KD) But in the sense of forecasting; actually telling
when and where events will occur,

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(KD) actually it's not really possible.

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(KD) The more we try to narrow down predictions,


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(KD) the more we're running the risk of false positives.

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(HF) You need a few ingredients to create a
mathematical model:

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(HF) Start with some good data, and then spot the
underlying pattern.

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(HF) Finally, pinpoint which vital features in the data
create that pattern,

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(HF) and everything else, you can strip out.

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(HF) When it comes to terrorism, this if fine if all you
want to do is explain the big relationships,

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(HF) or look at the long term,

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(HF) but, according to Karsten Donnay, this
simplification limits the kind of predictions

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(HF) that you can make.

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(KD) What you can use this model effectively for
at the moment -

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(KD) and I think this is what a lot of the research is
about -

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(KD) [is] to understand fundamental dynamics that
are ongoing.

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(KD) And this is always looking into the past.

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(KD) But of course, if we understand these dynamics,
we can make at least qualitative assessments

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(KD) of what might happen in the future,

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(KD) but making a quantitative prediction requires much
more than getting the general gist right;

199
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(KD) you have to really understand what are the driving
motives of when and where things happen,

200
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(KD) and some of it is actually governed by chance - it's
coincidence, the way it plays out -


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(KD) and this is something which is systematically
extremely hard to forecast. (14:50)