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(Female announcer) Governments worldwide battle to control and contain terrorism.
Police and the courts struggle to separate harmless loners from dangerous lone wolves.
Opinions differ on the most effective way to combat terrorist attacks,
from military interventions on the ground, to curbing political and religious radicalisation.
But in this edition of Discovery, we'll be hearing about a more unusual new weapon
that might be used in the future to fight terrorism:
maths (1:00)
(A) We were looking at the data in a new way, we were using tools that were somewhat foreign,
(A) these were tools that came out of physics and complex systems, not tools that necessarily came out of the political science community.
(A) And we were saying things that were kind of weird.
(B) One thinks of terrorism as something very random, something so strange that it must be done in a very chaotic way.
(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.
(A) For terrorism, that had somewhat shocking implications.
(A)If you understand the frequencies of the small events, you can extrapolate,
(A) and then make a forecast out into the future, about what the probability should be
(A) for a very large event.
(HF) So, could maths predict the next 9/11?
(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;
(HF) a pattern that lies behind a host of diverse phenomena, from economics to earthquakes.
(HF) I'm Dr Hannah Fry, and I'm a mathematician from University College London, working on complex systems.
(HF) These are systems, like terrorism, which at first seem complex, and random
(HF) but if you stand back and study the bigger picture, then a surprising number of patterns can appear;
(HF) patterns which you can describe using mathematics.
(HF) Dr (?), a computer scientist at the University of Colorado, was one of the first to find a tangible, mathematical connection underlying terrorism.
(HF) He looked at 30,000 terror attacks worldwide, over 40 years
(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
(HF) and the results were remarkable.
(Dr) This initial analysis we did, it was quite shocking, we found this thing that looked like
(Dr) what's called a power law distribution, which is a very special kind of mathematical pattern that usually
(Dr) crops up in physics, in fact, but increasingly is observed in social and biological systems,
(Dr) and this is somewhat surprising, because when we think about terrorism,
(Dr) we think mainly about the capricious, highly contextualised nature of the individual actors
(Dr) that carry out these events,
(Dr) and yet, at the global level, we see this remarkable pattern, this power law pattern, emerge.
(HF) So it's obviously a bit tricky to describe a graph on the radio. (Dr) [Laughs] Yes.
(HF) but could you give us an idea of what a power law looks like,
(HF) perhaps, compared to some other distributions that people might be familiar with?
(Dr) So a power law distribution is very different from
(Dr) what most of us experience, and our intuition is built around, as human beings.
(Dr) Most of our world is wrapped up in what are called Gaussian, or normal, distributions.
(Dr) So, the range of heights that we experience among other humans,
(Dr) has what's called a normal distribution. (HF) Like a bell curve.
(Dr) [Confirming] Like a bell curve. Which means that there's an average,
(Dr) that is representative of essentially the entire population.
(NJ) One of the first graphs that we ever draw in school is one of heights of people in the classroom.
(HF) Neil Johnson, professor of Physics at the University of Miami.
(NJ) There's usually some great big peak, and there's a little bit of spreading either side of the peak,
(NJ) Might be something like, you know, for adults, 5 foot 6 or something like this,
(NJ) that's the average, and of course people have wide variation; basketball players, and there's also
(NJ) people who are much shorter, but nobody's a foot tall in the adult population, and nobody's 20 feet tall.
(NJ) Well, that's not how it works for the severity of attacks.
(NJ) You might think it would have, you know, in an attack, people use an explosive device.
(NJ) You might think it blows up a typical number of people, you know, plus or minus 3.
(NJ) But no, it's a completely different distribution.
(NJ) It is the equivalent of having the 20 foot person, and the 1 foot person happening pretty frequently.
(HF) A power law curve looks like the downward slope of a hill.
(HF) At the top left, you have a large number of small attacks that kill a few people,
(HF) and at the bottom right, you have a tiny number of events that are very severe,
(HF) with hundreds, or thousands of deaths.
(HF) Behind this graph lies a very simple equation, providing a clear mathematical link
(HF) between smalll, frequent attacks, and rare, large-scale strikes.
(HF) Now this shape has been found time and time again, over different decades, in different cities,
(HF) and for different terrorist groups.
(HF) And despite huge changes in global geopolitics,
(HF) from the fall of the Soviet Union to the rise of Islamic extremism,
(HF) this simple mathematical pattern has persisted.
(Dr) The remarkable thing about the power law distribution in the sizes of terrorist events,
(Dr) is that it seems to be very robust, so it suggests that this may be a fundamental pattern,
(Dr) it may be that the nature of the modern world produces this pattern,
(Dr) so from a policy perspective, there is an implication that changing this pattern,
(Dr) being able to reduce the likelihood of a large terrorist even like 9/11 happening again
(Dr) may be not as simple as finding the terrorists and throwing them in jail.
(Dr) It may be more subtle, it may be that the nature of the global system
(Dr) tends to produce the types of individuals that would then go about carrying out
(Dr) these kinds of events.
(Dr) And that's a much harder problem to solve from a policy perspective.
(HF) So how easy was it for you to get your work published on this?
(Dr) (laughs) (HF) (laughs)
(Dr) I'm laughing because it was not easy. (HF) Yeah.
(Dr) My colleague, Maxwell, and I started this work in 2003, when the Iraq invasion
(Dr) was really getting going,
(Dr) and the paper was not published until 2007.
(Dr) There were many factors that made it difficult, but I think one of them was that this was
(Dr) such a weird take on a problem that people had been thinking about for a long time.
(Dr) Political scientists have been studying terrorism for decades,
(Dr) so we were looking at the data in a new way,
(Dr) we were talking about terrorism not as a phenomenon of decision making,
(Dr) but almost as a natural phenomenon.
(Dr) This idea that we could look at the entire world almost as a natural kind of system,
(Dr) and characterise its patterns without having to refer to the actual decisions that produced the events.
(Dr) So the unpleasant aspect of trying to get this work published is that we tried 10 different journals
(HF) Wow. (Dr) in order to get this published,
(Dr) and sometimes the reviews we got back from academics, they seemed to be
(Dr) missing the point, in some ways.
(Dr) They didn't understand what we were doing, or what the results implied.
(HF) So I understand one of the really important implications is about really large events.
(HF) What did you find there?
(Dr) The fact that the power law pattern exists,
(Dr) and the implication that these are all part of the same fundamental process,
(Dr) it does imply that the largest events, things like 9/11,
(Dr) will occur with surprising frequency, and the mathematical function is strong enough
(Dr) that one can actually extrapolate, and then make a forecast in much the same way
(Dr) that forecasts are made for earthquakes.
(Dr) In fact, the power law distribution is the same distribution
(Dr) that characterises the frequency of earthquakes, and the frequency of terrorist events.
(Dr) The shape of the distribution is slightly different, but the pattern is the same.
(Dr) And so, by applying this mathematical model to forecasting, we can make an estimate
(Dr) of the probability that we should see an event in the next 10 years, for instance,
(Dr) that kills as many, or more people as 9/11 did.
(HF) And what did you find?
(Dr) The likelihood across the set of models that we fitted to the data, over the next 10 years,
(Dr) is somewhere around 30%, which is not a certainty,
(Dr) but it's still an uncomfortably high number.
(N1) At least a hundred people are reported killed, and five hundred injured
(N1) in a chain of car bomb attacks across Bombay.
(HF) In 1993, 13 bombs exploded within 3 hours in Bombay, and at the final count, over 1500 people
(HF) were killed or injured.
(N2) Russia observes two days of national mourning for the many victims of Beslan.
(N2) More than 100 funerals take place in one day, attended by thousands of people.
(HF) The Beslan school siege in 2004, carried out by Chechen rebels,
(HF) hit over 1000 children, parents, and teachers.
(HF) And, after 9/11 - the largest terrorist attack in human history, which killed almost 3000 people -
(HF) funding was ploughed into new, scientific ways to try and tackle terrorism,
(HF) from using Game Theory in airport security to analysing the social networks of terror suspects.
(HF) But now, researchers are using data on terrorism in insurgencies to try and forecast future attacks.
(HF) Physicist, Neil Johnson, from the University of Miami, studied the timings between
(HF) terrorist events in one area, and, strangely enough,
(HF )the same kind of power law pattern lay behind this data too.
(NJ) Our initial study was looking at a few regions in Afghanistan, and Iraq.
(NJ) We've now done the study across basically every country where we could find data -
(NJ) that includes Africa, includes suicide bombings of Hezbollah
(NJ) we've looked at suicide attacks in Pakistan,
(NJ) they all seem to follow this relationship.
(HF) So if this happened then, for example, in a UK city, how confident could you be
(HF) in predicting the timing of the next attack.
(NJ) Yeah, of course it will never be down to the day;
(NJ) it will be, in some situa- like, you know- if it's down to the week.
(NJ) But what can be very useful is predicting the trend.
(NJ) Are we going to see the events get less frequent in time?
(NJ) Are we going to see them get more frequent?
(NJ) And if we see them get more frequent, roughly how many are we going to be getting
(NJ) every few weeks?
(NJ) It's not meant to be like predicting, you know whether it's going to rain in the next three days,
(NJ) it's meant to be some trend, and I very much see it in that analogy with say, weather prediction.
(NJ) The medium-term weather forecasts are getting better and better,
(NJ) but it's still very hard to say that at 5 o' clock, in three days,
(NJ) rain will fall on a particular place in London.
(NJ) But we're all very interested, and very keen, to know when some front is moving through,
(NJ) and over the next three days, there'll be some increase in the trend of rain.
(NJ) That is a very useful statement.
(NJ) And it's exactly that level [of] prediction that we believe that this type of work is good for.
(NJ) It's never going to say that in five days' time, [in] a particular place, there'll be a particular attack,
(NJ) but what it is saying is: wait a minute, this group, in this region of a country,
(NJ) they are escalating.
(HF) So I suppose it goes without saying then, that these ideas would be incredibly useful
(HF) to counter-terrorism agencies, but how much interest have they shown in your research?
(NJ) Well, I'm currently funded by the Office of Naval Research,
(NJ) they've been very supportive, they're very interested in this.
(NJ) I've also had funding through another agency which was interested in counter-IED strategies.
(NJ) So I would say that there's been a lot of interest,
(NJ) and we've even had interest, I remember getting an email from Marines
(NJ) in a forward-operating base in Afghanistan, telling me that they'd been trying -
(NJ) because the formula is so simple, the mathematics is actually so simple -
(NJ) that they'd been trying out this particular analysis of successive events that
(NJ) they'd actually been seeing, and experiencing around them.
(HF) Wow. So Marines in the field have been in contact with you, talking about your mathematical models, then?
(NJ) Yeah, the intelligence officer from one of the units, yes.
(HF) But not everyone is convinced that we can make such precise predictions.
(HF) Dr Karsten Donnay is a social scientist from the Swiss Federal Institute of Technology,
(HF) who specialises in conflict modelling and simulation.
(HF) He thinks there's a danger that these models can be taken too far.
(KD) I think one has to be very careful about using this for direct prediction,
(KD) I mean we do distinguish between a prediction and forecasting.
(KD) If you talk about long-term predictions, then it's feasible to make statements like this:
(KD) There's (??) this chance that in the next 10 years, an event of a certain size will occur,
(KD) that's definitely possible.
(KD) But in the sense of forecasting; actually telling when and where events will occur,
(KD) actually it's not really possible.
(KD) The more we try to narrow down predictions,
(KD) the more we're running the risk of false positives.
(HF) You need a few ingredients to create a mathematical model:
(HF) Start with some good data, and then spot the underlying pattern.
(HF) Finally, pinpoint which vital features in the data create that pattern,
(HF) and everything else, you can strip out.
(HF) When it comes to terrorism, this if fine if all you want to do is explain the big relationships,
(HF) or look at the long term,
(HF) but, according to Karsten Donnay, this simplification limits the kind of predictions
(HF) that you can make.
(KD) What you can use this model effectively for at the moment -
(KD) and I think this is what a lot of the research is about -
(KD) [is] to understand fundamental dynamics that are ongoing.
(KD) And this is always looking into the past.
(KD) But of course, if we understand these dynamics, we can make at least qualitative assessments
(KD) of what might happen in the future,
(KD) but making a quantitative prediction requires much more than getting the general gist right;
(KD) you have to really understand what are the driving motives of when and where things happen,
(KD) and some of it is actually governed by chance - it's coincidence, the way it plays out -
(KD) and this is something which is systematically extremely hard to forecast. (14:50)