9:59:59.000,9:59:59.000
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9:59:59.000,9:59:59.000
(Female announcer) Governments worldwide battle to control and contain terrorism.

9:59:59.000,9:59:59.000
Police and the courts struggle to separate harmless loners from dangerous lone wolves.

9:59:59.000,9:59:59.000
Opinions differ on the most effective way to combat terrorist attacks,

9:59:59.000,9:59:59.000
from military interventions on the ground, to curbing political and religious radicalisation.

9:59:59.000,9:59:59.000
But in this edition of Discovery, we'll be hearing about a more unusual new weapon

9:59:59.000,9:59:59.000
that might be used in the future to fight terrorism:

9:59:59.000,9:59:59.000
maths (1:00)

9:59:59.000,9:59:59.000
(A) We were looking at the data in a new way, we were[br]using tools that were somewhat foreign,

9:59:59.000,9:59:59.000
(A) these were tools that came out of physics[br]and complex systems, not tools that necessarily came out of the political science community.

9:59:59.000,9:59:59.000
(A) And we were saying things that were kind of weird.

9:59:59.000,9:59:59.000
(B) One thinks of terrorism as something very random, [br]something so strange that it must be done in a very[br]chaotic way.

9:59:59.000,9:59:59.000
(B) But of course, in the end, it is an activity, it's a[br]human activity, so it's quite interesting then that the[br]patterns that you seen in the events are not random.

9:59:59.000,9:59:59.000
(A) For terrorism, that had somewhat shocking implications.

9:59:59.000,9:59:59.000
(A)If you understand the frequencies of the small [br]events, you can extrapolate,

9:59:59.000,9:59:59.000
(A) and then make a forecast out into the future, [br]about what the probability should be

9:59:59.000,9:59:59.000
(A) for a very large event.

9:59:59.000,9:59:59.000
(HF) So, could maths predict the next 9/11?

9:59:59.000,9:59:59.000
(HF) You're listening to the BBC World Service, and today[br]on Discovery, I'll be looking at the hidden mathematical[br]pattern that is being discovered in global terrorism;

9:59:59.000,9:59:59.000
(HF) a pattern that lies behind a host of diverse phenomena,[br]from economics to earthquakes.

9:59:59.000,9:59:59.000
(HF) I'm Dr Hannah Fry, and I'm a mathematician from[br]University College London, working on complex systems.

9:59:59.000,9:59:59.000
(HF) These are systems, like terrorism, which at first seem[br]complex, and random

9:59:59.000,9:59:59.000
(HF) but if you stand back and study the bigger picture, then[br]a surprising number of patterns can appear;

9:59:59.000,9:59:59.000
(HF) patterns which you can describe using mathematics.

9:59:59.000,9:59:59.000
(HF) Dr (?), a computer scientist at the University of[br]Colorado, was one of the first to find a tangible,[br]mathematical connection underlying terrorism.

9:59:59.000,9:59:59.000
(HF) He looked at 30,000 terror attacks worldwide, over[br]40 years

9:59:59.000,9:59:59.000
(HF) and for all of the events, he counted how many times a[br]certain number of people were killed, and plotted it on a graph[br]

9:59:59.000,9:59:59.000
(HF) and the results were remarkable.

9:59:59.000,9:59:59.000
(Dr) This initial analysis we did, it was quite shocking,[br]we found this thing that looked like

9:59:59.000,9:59:59.000
(Dr) what's called a power law distribution, which is a [br]very special kind of mathematical pattern that usually

9:59:59.000,9:59:59.000
(Dr) crops up in physics, in fact, but increasingly is [br]observed in social and biological systems,

9:59:59.000,9:59:59.000
(Dr) and this is somewhat surprising, because when we [br]think about terrorism,

9:59:59.000,9:59:59.000
(Dr) we think mainly about the capricious, highly [br]contextualised nature of the individual actors

9:59:59.000,9:59:59.000
(Dr) that carry out these events,

9:59:59.000,9:59:59.000
(Dr) and yet, at the global level, we see this remarkable[br]pattern, this power law pattern, emerge.

9:59:59.000,9:59:59.000
(HF) So it's obviously a bit tricky to describe a graph[br]on the radio. (Dr) [Laughs] Yes.

9:59:59.000,9:59:59.000
(HF) but could you give us an idea of what a power law[br]looks like,

9:59:59.000,9:59:59.000
(HF) perhaps, compared to some other distributions that[br]people might be familiar with?

9:59:59.000,9:59:59.000
(Dr) So a power law distribution is very different from[br]

9:59:59.000,9:59:59.000
(Dr) what most of us experience, and our intuition [br]is built around, as human beings.

9:59:59.000,9:59:59.000
(Dr) Most of our world is wrapped up in what are called[br]Gaussian, or normal, distributions.

9:59:59.000,9:59:59.000
(Dr) So, the range of heights that we experience[br]among other humans,

9:59:59.000,9:59:59.000
(Dr) has what's called a normal distribution.[br](HF) Like a bell curve.

9:59:59.000,9:59:59.000
(Dr) [Confirming] Like a bell curve. Which means that[br]there's an average,

9:59:59.000,9:59:59.000
(Dr) that is representative of essentially the entire population.

9:59:59.000,9:59:59.000
(NJ) One of the first graphs that we ever draw in[br]school is one of heights of people in the classroom.

9:59:59.000,9:59:59.000
(HF) Neil Johnson, professor of Physics at the[br]University of Miami.

9:59:59.000,9:59:59.000
(NJ) There's usually some great big peak, and there's a[br]little bit of spreading either side of the peak,

9:59:59.000,9:59:59.000
(NJ) Might be something like, you know, for adults,[br]5 foot 6 or something like this,

9:59:59.000,9:59:59.000
(NJ) that's the average, and of course people have wide[br]variation; basketball players, and there's also

9:59:59.000,9:59:59.000
(NJ) people who are much shorter, but nobody's a foot[br]tall in the adult population, and nobody's 20 feet tall.

9:59:59.000,9:59:59.000
(NJ) Well, that's not how it works for the severity of[br]attacks.

9:59:59.000,9:59:59.000
(NJ) You might <i>think</i> it would have, you know, in an[br]attack, people use an explosive device.

9:59:59.000,9:59:59.000
(NJ) You might <i>think</i> it blows up a typical number of[br]people, you know, plus or minus 3.

9:59:59.000,9:59:59.000
(NJ) But no, it's a completely different distribution.

9:59:59.000,9:59:59.000
(NJ) It is the equivalent of having the 20 foot person,[br]and the 1 foot person happening pretty frequently.

9:59:59.000,9:59:59.000
(HF) A power law curve looks like the downward slope[br]of a hill.

9:59:59.000,9:59:59.000
(HF) At the top left, you have a large number of small[br]attacks that kill a few people,

9:59:59.000,9:59:59.000
(HF) and at the bottom right, you have a tiny number of events that are very severe,

9:59:59.000,9:59:59.000
(HF) with hundreds, or thousands of deaths.

9:59:59.000,9:59:59.000
(HF) Behind this graph lies a very simple equation,[br]providing a clear mathematical link

9:59:59.000,9:59:59.000
(HF) between smalll, frequent attacks, and rare,[br]large-scale strikes.

9:59:59.000,9:59:59.000
(HF) Now this shape has been found time and time[br]again, over different decades, in different cities,

9:59:59.000,9:59:59.000
(HF) and for different terrorist groups.

9:59:59.000,9:59:59.000
(HF) And despite huge changes in global geopolitics,

9:59:59.000,9:59:59.000
(HF) from the fall of the Soviet Union to the rise of[br]Islamic extremism,

9:59:59.000,9:59:59.000
(HF) this simple mathematical pattern has persisted.

9:59:59.000,9:59:59.000
(Dr) The remarkable thing about the power law[br]distribution in the sizes of terrorist events,

9:59:59.000,9:59:59.000
(Dr) is that it seems to be very robust, so it suggests that[br]this may be a fundamental pattern,

9:59:59.000,9:59:59.000
(Dr) it may be that the nature of the modern world[br]produces this pattern,

9:59:59.000,9:59:59.000
(Dr) so from a policy perspective, there is an[br]implication that changing this pattern,

9:59:59.000,9:59:59.000
(Dr) being able to reduce the likelihood of a large[br]terrorist even like 9/11 happening again

9:59:59.000,9:59:59.000
(Dr) may be not as simple as finding the terrorists and[br]throwing them in jail.

9:59:59.000,9:59:59.000
(Dr) It may be more subtle, it may be that the nature of[br]the global system

9:59:59.000,9:59:59.000
(Dr) tends to produce the types of individuals that would then go about carrying out

9:59:59.000,9:59:59.000
(Dr) these kinds of events.

9:59:59.000,9:59:59.000
(Dr) And that's a much harder problem to solve from[br]a policy perspective.

9:59:59.000,9:59:59.000
(HF) So how easy was it for you to get your work[br]published on this?

9:59:59.000,9:59:59.000
(Dr) (laughs)[br](HF) (laughs)

9:59:59.000,9:59:59.000
(Dr) I'm laughing because it was not easy.[br](HF) Yeah.

9:59:59.000,9:59:59.000
(Dr) My colleague, Maxwell, and I started this work in[br]2003, when the Iraq invasion

9:59:59.000,9:59:59.000
(Dr) was really getting going,

9:59:59.000,9:59:59.000
(Dr) and the paper was not published until 2007.

9:59:59.000,9:59:59.000
(Dr) There were many factors that made it difficult, but[br]I think one of them was that this was

9:59:59.000,9:59:59.000
(Dr) such a weird take on a problem that people had[br]been thinking about for a long time.

9:59:59.000,9:59:59.000
(Dr) Political scientists have been studying terrorism for[br]decades,

9:59:59.000,9:59:59.000
(Dr) so we were looking at the data in a new way,

9:59:59.000,9:59:59.000
(Dr) we were talking about terrorism not as a[br]phenomenon of decision making,

9:59:59.000,9:59:59.000
(Dr) but almost as a natural phenomenon.

9:59:59.000,9:59:59.000
(Dr) This idea that we could look at the entire world[br]almost as a natural kind of system,

9:59:59.000,9:59:59.000
(Dr) and characterise its patterns without having to refer[br]to the actual decisions that produced the events.

9:59:59.000,9:59:59.000
(Dr) So the unpleasant aspect of trying to get this[br]work published is that we tried 10 different journals

9:59:59.000,9:59:59.000
(HF) Wow.[br](Dr) in order to get this published,

9:59:59.000,9:59:59.000
(Dr) and sometimes the reviews we got back from[br]academics, they seemed to be

9:59:59.000,9:59:59.000
(Dr) missing the point, in some ways.

9:59:59.000,9:59:59.000
(Dr) They didn't understand what we were doing,[br]or what the results implied.

9:59:59.000,9:59:59.000
(HF) So I understand one of the really important[br]implications is about really large events.

9:59:59.000,9:59:59.000
(HF) What did you find there?

9:59:59.000,9:59:59.000
(Dr) The fact that the power law pattern exists,

9:59:59.000,9:59:59.000
(Dr) and the implication that these are all part of[br]the same fundamental process,

9:59:59.000,9:59:59.000
(Dr) it does imply that the largest events, things like 9/11,

9:59:59.000,9:59:59.000
(Dr) will occur with surprising frequency, and the[br]mathematical function is strong enough

9:59:59.000,9:59:59.000
(Dr) that one can actually extrapolate, and then make a[br]forecast in much the same way

9:59:59.000,9:59:59.000
(Dr) that forecasts are made for earthquakes.

9:59:59.000,9:59:59.000
(Dr) In fact, the power law distribution is the same[br]distribution

9:59:59.000,9:59:59.000
(Dr) that characterises the frequency of earthquakes,[br]and the frequency of terrorist events.

9:59:59.000,9:59:59.000
(Dr) The shape of the distribution is slightly different,[br]but the pattern is the same.

9:59:59.000,9:59:59.000
(Dr) And so, by applying this mathematical model to[br]forecasting, we can make an estimate

9:59:59.000,9:59:59.000
(Dr) of the probability that we should see an event in the[br]next 10 years, for instance,

9:59:59.000,9:59:59.000
(Dr) that kills as many, or more people as 9/11 did.

9:59:59.000,9:59:59.000
(HF) And what did you find?

9:59:59.000,9:59:59.000
(Dr) The likelihood across the set of models that we[br]fitted to the data, over the next 10 years,

9:59:59.000,9:59:59.000
(Dr) is somewhere around 30%, which is not a [br]certainty,

9:59:59.000,9:59:59.000
(Dr) but it's still an uncomfortably high number.

9:59:59.000,9:59:59.000
(N1) At least a hundred people are reported killed, and[br]five hundred injured

9:59:59.000,9:59:59.000
(N1) in a chain of car bomb attacks across Bombay.

9:59:59.000,9:59:59.000
(HF) In 1993, 13 bombs exploded within 3 hours in[br]Bombay, and at the final count, over 1500 people

9:59:59.000,9:59:59.000
(HF) were killed or injured.

9:59:59.000,9:59:59.000
(N2) Russia observes two days of national mourning[br]for the many victims of Beslan.

9:59:59.000,9:59:59.000
(N2) More than 100 funerals take place in one day,[br]attended by thousands of people.

9:59:59.000,9:59:59.000
(HF) The Beslan school siege in 2004, carried out by[br]Chechen rebels,

9:59:59.000,9:59:59.000
(HF) hit over 1000 children, parents, and teachers.

9:59:59.000,9:59:59.000
(HF) And, after 9/11 - the largest terrorist attack in[br]human history, which killed almost 3000 people -

9:59:59.000,9:59:59.000
(HF) funding was ploughed into new, scientific ways[br]to try and tackle terrorism,

9:59:59.000,9:59:59.000
(HF) from using Game Theory in airport security[br]to analysing the social networks of terror suspects.

9:59:59.000,9:59:59.000
(HF) But now, researchers are using data on terrorism[br]in insurgencies to try and forecast future attacks.

9:59:59.000,9:59:59.000
(HF) Physicist, Neil Johnson, from the University of[br]Miami, studied the timings between

9:59:59.000,9:59:59.000
(HF) terrorist events in one area, and, strangely enough,

9:59:59.000,9:59:59.000
(HF )the same kind of power law pattern lay behind this data too.

9:59:59.000,9:59:59.000
(NJ) Our initial study was looking at a few regions in[br]Afghanistan, and Iraq.

9:59:59.000,9:59:59.000
(NJ) We've now done the study across basically every[br]country where we could find data -

9:59:59.000,9:59:59.000
(NJ) that includes Africa, includes suicide bombings[br]of Hezbollah

9:59:59.000,9:59:59.000
(NJ) we've looked at suicide attacks in Pakistan,

9:59:59.000,9:59:59.000
(NJ) they all seem to follow this relationship.

9:59:59.000,9:59:59.000
(HF) So if this happened then, for example, in a UK[br]city, how confident could you be

9:59:59.000,9:59:59.000
(HF) in predicting the timing of the next attack.

9:59:59.000,9:59:59.000
(NJ) Yeah, of course it will never be down to the day;

9:59:59.000,9:59:59.000
(NJ) it will be, in some situa- like, you know- if it's down[br]to the week.

9:59:59.000,9:59:59.000
(NJ) But what can be very useful is predicting the trend.

9:59:59.000,9:59:59.000
(NJ) Are we going to see the events get less[br]frequent in time?

9:59:59.000,9:59:59.000
(NJ) Are we going to see them get more frequent?

9:59:59.000,9:59:59.000
(NJ) And if we see them get more frequent, roughly[br]how many are we going to be getting

9:59:59.000,9:59:59.000
(NJ) every few weeks?

9:59:59.000,9:59:59.000
(NJ) It's not meant to be like predicting, you know[br]whether it's going to rain in the next three days,

9:59:59.000,9:59:59.000
(NJ) it's meant to be some trend, and I very much see it[br]in that analogy with say, weather prediction.

9:59:59.000,9:59:59.000
(NJ) The medium-term weather forecasts are getting[br]better and better,

9:59:59.000,9:59:59.000
(NJ) but it's still very hard to say that at 5 o' clock,[br]in three days,

9:59:59.000,9:59:59.000
(NJ) rain will fall on a particular place in London.

9:59:59.000,9:59:59.000
(NJ) But we're all very interested, and very keen, to[br]know when some front is moving through,

9:59:59.000,9:59:59.000
(NJ) and over the next three days, there'll be some[br]increase in the trend of rain.

9:59:59.000,9:59:59.000
(NJ) That is a very useful statement.

9:59:59.000,9:59:59.000
(NJ) And it's exactly that level [of] prediction that we[br]believe that this type of work is good for.

9:59:59.000,9:59:59.000
(NJ) It's never going to say that in five days' time,[br][in] a particular place, there'll be a particular attack,

9:59:59.000,9:59:59.000
(NJ) but what it is saying is: wait a minute, <i>this</i> group,[br]in <i>this</i> region of a country,

9:59:59.000,9:59:59.000
(NJ) <i>they</i> are escalating.

9:59:59.000,9:59:59.000
(HF) So I suppose it goes without saying then, that[br]these ideas would be incredibly useful

9:59:59.000,9:59:59.000
(HF) to counter-terrorism agencies, but how much[br]interest have they shown in your research?

9:59:59.000,9:59:59.000
(NJ) Well, I'm currently funded by the Office of Naval[br]Research,

9:59:59.000,9:59:59.000
(NJ) they've been very supportive, they're very[br]interested in this.

9:59:59.000,9:59:59.000
(NJ) I've also had funding through another agency[br]which was interested in counter-IED strategies.

9:59:59.000,9:59:59.000
(NJ) So I would say that there's been a lot of interest,

9:59:59.000,9:59:59.000
(NJ) and we've even had interest, I remember getting[br]an email from Marines

9:59:59.000,9:59:59.000
(NJ) in a forward-operating base in Afghanistan, telling[br]me that they'd been trying -

9:59:59.000,9:59:59.000
(NJ) because the formula is so simple, the mathematics[br]is actually so simple -

9:59:59.000,9:59:59.000
(NJ) that they'd been trying out this particular analysis[br]of successive events that

9:59:59.000,9:59:59.000
(NJ) they'd actually been seeing, and experiencing[br]around them.

9:59:59.000,9:59:59.000
(HF) Wow. So Marines in the field have been in contact[br]with you, talking about your mathematical models, then?

9:59:59.000,9:59:59.000
(NJ) Yeah, the intelligence officer from one of the[br]units, yes.

9:59:59.000,9:59:59.000
(HF) But not everyone is convinced that we can make[br]such precise predictions.

9:59:59.000,9:59:59.000
(HF) Dr Karsten Donnay is a social scientist from[br]the Swiss Federal Institute of Technology,

9:59:59.000,9:59:59.000
(HF) who specialises in conflict modelling and[br]simulation.

9:59:59.000,9:59:59.000
(HF) He thinks there's a danger that these models can[br]be taken too far.

9:59:59.000,9:59:59.000
(KD) I think one has to be very careful about using[br]this for direct prediction,

9:59:59.000,9:59:59.000
(KD) I mean we do distinguish between a prediction[br]and forecasting.

9:59:59.000,9:59:59.000
(KD) If you talk about long-term predictions, then it's[br]feasible to make statements like this:

9:59:59.000,9:59:59.000
(KD) There's (??) this chance that in the next 10 years, an event of a certain size will occur,

9:59:59.000,9:59:59.000
(KD) that's definitely possible.

9:59:59.000,9:59:59.000
(KD) But in the sense of forecasting; actually telling[br]when and where events will occur,

9:59:59.000,9:59:59.000
(KD) actually it's not really possible.

9:59:59.000,9:59:59.000
(KD) The more we try to narrow down predictions,[br]

9:59:59.000,9:59:59.000
(KD) the more we're running the risk of false positives.

9:59:59.000,9:59:59.000
(HF) You need a few ingredients to create a[br]mathematical model:

9:59:59.000,9:59:59.000
(HF) Start with some good data, and then spot the[br]underlying pattern.

9:59:59.000,9:59:59.000
(HF) Finally, pinpoint which vital features in the data[br]create that pattern,

9:59:59.000,9:59:59.000
(HF) and everything else, you can strip out.

9:59:59.000,9:59:59.000
(HF) When it comes to terrorism, this if fine if all you[br]want to do is explain the big relationships,

9:59:59.000,9:59:59.000
(HF) or look at the long term,

9:59:59.000,9:59:59.000
(HF) but, according to Karsten Donnay, this[br]simplification limits the kind of predictions

9:59:59.000,9:59:59.000
(HF) that you can make.

9:59:59.000,9:59:59.000
(KD) What you can use this model effectively for[br]at the moment -

9:59:59.000,9:59:59.000
(KD) and I think this is what a lot of the research is[br]about -

9:59:59.000,9:59:59.000
(KD) [is] to understand fundamental dynamics that[br]are ongoing.

9:59:59.000,9:59:59.000
(KD) And this is always looking into the past.

9:59:59.000,9:59:59.000
(KD) But of course, if we understand these dynamics,[br]we can make at least qualitative assessments

9:59:59.000,9:59:59.000
(KD) of what might happen in the future,

9:59:59.000,9:59:59.000
(KD) but making a quantitative prediction requires much[br]more than getting the general gist right;

9:59:59.000,9:59:59.000
(KD) you have to really understand what are the driving[br]motives of when and where things happen,

9:59:59.000,9:59:59.000
(KD) and some of it is actually governed by chance - it's[br]coincidence, the way it plays out -[br]

9:59:59.000,9:59:59.000
(KD) and this is something which is systematically[br]extremely hard to forecast. (14:50)