In Our Time - Complexity

Episode Date: December 19, 2013

Melvyn Bragg and his guests discuss complexity and how it can help us understand the world around us. When living beings come together and act in a group, they do so in complicated and unpredictable ways: societies often behave very differently from the individuals within them. Complexity was a phenomenon little understood a generation ago, but research into complex systems now has important applications in many different fields, from biology to political science. Today it is being used to explain how birds flock, to predict traffic flow in cities and to study the spread of diseases.With:Ian Stewart Emeritus Professor of Mathematics at the University of WarwickJeff Johnson Professor of Complexity Science and Design at the Open UniversityProfessor Eve Mitleton-Kelly Director of the Complexity Research Group at the London School of Economics.Producer: Thomas Morris.

This BBC podcast is supported by ads outside the UK. Thank you for downloading this episode of In Our Time. For more details about In Our Time, and for our terms of use, please go to BBC.co.com.uk slash Radio 4. I hope you enjoy the programme. Hello, in the late 1940s a chemist in Brussels called Ilya Prigogine embarked on research which would take him in rather surprising directions. His work concerned, the energy associated with chemical reactions.

and in 1977 he won him a Nobel Prize in chemistry. But it also led him to write a book about traffic management, surely one of the more startling examples of the unexpected consequences of scientific research. Prygéin proved something which scientists before him had doubted that it's possible to create order from disorder. He realised that his ideas applied not just to chemical reactions, but to the wider world from city traffic problems to how a colony of ants organises itself.

Today this field of study is known as complexity. Complexity theories study the ways in which large groups of individuals behave collectively. Complexity only emerged as a separate discipline around 40 years ago, but today it used to study difficult problems fields such as diverse as biology and international politics to explain the way birds flock and how the economy works. The women to discuss complexity are Ian Stewart, Emeritus Professor of Mathematics at the University of Warwick, Jeff Johnson, Professor of Complexity Science and Design at the Open University,

and Professor Eve Middleton Kelly, director of the Complexity Research Group at the London School of Economics. Ian Stewart, would you begin by giving us a brief overview of what complexity is and how it's used? It's a mathematical technique. You can run computer simulations based on it, but also a point of view about systems

in which large numbers of individuals interact with each other. And it sounds very vague in general, so let's take some examples. Think of a crowd of people moving through a large building like a sports stadium. You have lots of people, they bump into each other, they are interacting with each other, and also with the building, they know where they want to go. Think of an epidemic. Now you have interactions between people where the interaction is exchanging the disease organism, it's catching the disease,

and the way the epidemic spreads depends on how all those interactions fit together. and a third example the London Stock Exchange people are buying and selling stocks and shares you have large numbers of traders and they're interacting by these exchanges of stocks and shares so at first sight those are very very different systems

and in detail they work in different ways but they have a lot in common and the common feature is this large group of agents or entities which are interacting with each other according to fairly specific rules. So the idea is to actually set up the mathematical model to represent that kind of system in a sort of fairly accurate way.

We're quite near the beginning of complexity theory studies, aren't we? In which ways do you think it'll be most useful? I think one of the main uses is bringing new ways of thinking into some of the big problems that face humanity. One of the reasons that this subject has got going is because increasingly we live in a world which is highly connected and what happens in a distant country might make a big difference. When the SARS epidemic got started in Hong Kong, the next place it went was Toronto.

That's because of air travel. So the structure of the world is changing and these big systems... The way we view the structure of the world is changing. The way we view it, but the structure itself is changing. The internet has changed a lot of things. That's another example of a complex system. And this is going to...

What do you complex theories hope to arrive at? As a mathematician, what we'd like to do is actually understand how the things work. Mathematicians would be interested in the basic principles. interested in not so much can we model the stock market, but things like what do various systems have in common, what are the general principles, how can we understand how these things behave? But from a more practical point of view, we would like to be able to do things like manage an epidemic better. This is a major problem. You know there's a disease coming,

foot and mouth disease in cattle. There was no question that this was around. the characteristics were pretty well understood. But what strategy should you use as a government to try and contain the outbreak best? So if you have mathematical models that are good enough, you can try strategies out on the models. You can do experiments in the models, which you cannot do in the real world,

and you can maybe learn how to deal with these problems. Jeff Johnson, can you give us an idea of the origins of this theory, how it developed. Yes, complex system science is a new way of thinking. It contrasts with 19th century view of science, which was much more mechanical and deterministic. As Ian says, in complex systems, the dynamics of the system generally emerges

from the interaction of the parts or the agents, and that's not necessarily predictable in the way that traditional science thinks it should be. And so the history, in my view, of complex system science starts in the 19th century and one of the major events in this science is the invention of the computer. So I would say that complex system science is very much computer enabled because we have to compute the interactions of the agents and find out the way that the system dynamics are evolving.

There's other things too which are part of complex system science. and really I think our outlook has changed a lot as what prediction means. So in the 1960s, the weather scientist Lawrence discovered that there are systems which are what's called very sensitive to initial conditions

and the weather is like this so that a slight change in the conditions at one time can mean the system would diverge greatly at another time. So our expectation of what we can predict about physical systems or social systems or any other system has changed a lot in that time.

And so the history goes, I would say that another big event in complex system science was the setting up of the Santa Fe Institute in United States. The Santa Fe Institute. So this for many years has been a focus for new ideas in complex system science where people are, investigating ideas like adaptation. So complex systems will adapt to a changing environment to systems which are autonomous, which are self-healing and stuff like that. Why does mathematics come in?

Ian stress the fundamental place that mathematics plays in this. Can you just bring that to the fore again, please? Yeah, I'd say that mathematics is very important because of the way we represent systems. So in my view, mathematics gives a preciseness. which often molecular language lacks. And also mathematics is important. It may or may not have important theorems

which we can apply in trying to understand how systems work. But mathematics sits very closely next to computing. And so mathematics can give us new kinds of data structures that we need for computing the dynamics of systems. Do you think that since you started doing this, since the computer's got more and more powerful, Since these people like yourselves got involved in thinking about this, do you think progress has to be made that you're better at this than you were 40 years ago?

Absolutely. I'm certain of that. It's close related but distinct from a phenomenon known as chaos theory. Can you distinguish between them for us? Yes, indeed. There's different kinds of theories of chaos, but one of them depends upon what I said earlier, this sensitivity to initial conditions. and so this is what Lorentz described as the butterfly effect

so that if a butterfly would flap its wings then potentially you could have a storm form somewhere which wouldn't form somewhere else I'm not... It's a lovely image is there scientific truth in that? Well, yes, I mean, like many things in complex system science, the metaphors are used and misused, which is a pity.

Is that misused or used? It's very often misused, but it's actually true that there are many systems where the changing natural conditions would change the outcome. So, for example, in social systems, there's the old Rhine that goes, for want of a nail, the shoe was lost, for want of a shoe, the horse was lost, for want of a horse, the knight was lost.

Kingdom was lost. And eventually the kingdom's lost, yes. And so this shows that even social systems, very slight changes in the starting positions can change things very much. So, for example, if you get up five minutes late, you might miss the bus and you miss the bus, you might miss another connection and miss your flight,

so something very small can end up in a very big change. So you're trying to crack that, are you? That minutiae of unexpectedness and an accident, you think that system, I'm not being mocking, I'm fascinated. Maybe this is going to blow the rest of the 21st century away, just like the electron blew the 19th century away, but was asleep for 30 years as it were.

So you think that you can get to the heart of these millions and billions of interconnections because you talk about units and that, but these are people behaving, well, badly, indifferently, lazily. I think it's more what Ian said. It's a question of understanding. So there are things that are, for all practical purposes, unpredictable. So one of the things about chaos is that as the system behaviour diverges, you get a kind of horizon beyond which a prediction doesn't. make any sense. So, for example, what is society going to look like in 300 years' time?

You can't know that. But it's also understanding the limitations. So we human beings do things which are very unwise and very dangerous, that this kind of science can help us understand which parts of the future are safe and which parts are dangerous and we can adjust our policy accordingly. Can we distinguish Eve Middleton-Calli between the word complexity? and the idea behind it and the word complicated and the idea behind that is there a distinction

if so can you tell us what it is? Absolutely we need to make in fact a very clear distinction because we often confuse the one for the other so complicated is very much

a machine type system is something that and I've got three criteria to distinguish them in a complicated system we can design we can predict its behavior

and we can control its behavior. We can do none of these things with a complex system. So can you give us a good example of a complicated system? A complicated system would be, for example, a jet engine that has many, many parts interacting with each other. The fact that it has many parts interacting does not make it complex. It's making it complicated. So we can actually design a jet engine.

We can predict its behavior and we can control this behavior. Now, one of the key things that distinguishes the two is one of the insights that came from Ilya Prigugin, the person you introduced this notion with. What in fact he found was that complex systems can, in the jargon, create new order. They can create something new, a new structure, a new way of working, a new way of relating. which complicated systems cannot do. So this is at the heart of it, this is their distinguishing feature. How can they create new systems?

Is there any basic rule? You said they create new structures. The system will create a new structure. It is how they interact. A new structure can emerge through a different kind of interaction. I'm afraid it would be very useful for me if you give us examples. Indeed.

I am a social scientist and therefore I need to look at it from a different perspective than our two mathematicians. I work with very much with humans, with organisations, with governments and so on.

So for example, when you've got an uprising and the The Arab Spring. The Arab Spring. This is very much how a complex system is, I'm going to use another term here. That's all right.

We can do terms. We can explore it later. It is pushed away from equilibrium in the sense that it can no longer carry on existing, operating, under the old quote's regime. again in the technical term, what it means is it needs to explore new ways of being. And in that exploration, it will actually create those new structures, new ways of relating, new ways of operating.

If it doesn't, it will die. One of the basic qualities of complex system is connectivity. Yes. Can you say how that word fits into complex theory? Absolutely. because complex systems interact with each other, it is that we need to start with this idea of interaction. And I think as both Ian and Jeff have already said,

through entities interacting, and by entities I mean it could be individuals, groups, whole societies. When entities interact, they create complex behavior and they start connecting with each other. It is not only the matter of connection, it's also the matter of interdependence that then arises from that connectivity. You wanted to pop in for a moment, yeah.

I just wanted to take Eid to task. You said you can't design a complex system. I don't agree with that. I think if you take, for example, cities, cities are designed. They're an interesting area of design because they're never finished. but cities are certainly complex systems and I could give you many other examples

so let's not say that cities also evolve and they are and they are actually an example of what Eve is talking about you have people they can build buildings

they can make roads they have certain things that as individuals or groups they can do and out of this emerges a structure and cities are partly planned partly evolved, but they're planned to fit the sort of things that they evolved

into historically. You need transportation, you need places to stay, you need a whole pile of things which are sort of higher level structures. Do you have to come back in here? Yes, I would. Because I think this idea of design is very interesting.

I don't mean that you cannot design full stop. You need to take the three criteria together. Not design in the sense of both predict the behavior and control the behavior. This is the sense in which I was taking it. Yes, of course we can design. And we're always trying to design.

But in a lot of designs, the designs of complex systems, we have to allow for a great deal of uncertainty, unpredictability, and the system evolving. That is in the sense in which I meant it. Okay, well, we can agree on that. Ian, can we take on this notion of connectivity? and tell us how that plays out further in a complex system. The, you can, a lot of complex systems,

you can actually represent the connectivity as a kind of network. So, for example, in an epidemic, you have individuals who may or may not get the disease, they may be carrying the disease and be infectious, they may be immune to the disease, they may be dead. And at any given time, when the disease is spreading, it spreads when people come into contact with other people. So if I am not in contact with a particular person, then they can't transmit the disease to me.

This is actually fairly clear. But what it means is that in the abstract, you could draw a network showing all of the individuals and all of the people that they are actually in contact with, and the disease spreads along that network. It's like people moving through a building along corridors. And the structure of that network affects very strongly how fast the disease will spread and where it will spread too. If we're very highly connected, one infectious person can infect a very large number of people. If the average number of contacts between people is much lower,

the disease may spread more slowly. You wanted to... Yes, I did. I wanted to add to what Ian said, because we often assume things like connectivity are the same over time. They're not. That the quality, the intensity of connectivity varies all the time. And we need, again, to understand that connectivity is not the same, even with the same individuals over time.

It does vary. Jeff Johnson, we've got connectivity also that leads to something known as feedback. Are these terms of, well, obviously they're useful. What does this mean? How does this work in with your theory? Well, feedback is very natural, and I'm sure almost everybody experiences at all the time. So much of our social interaction is through networks, as has just been said. So you can imagine that if one person begins to spread a rumor about something, so person A can say to person B that something is true,

person B would tell person C, person C tells person D. Person D then tells person A, and person A says, aha, it was true after all. And so just as Eve says, the network's changing now because we've now got some positive feedback. And so the rumour, even if it's completely untrue, can spread that way. So that's one thing.

But very often in these networks, you've got all kinds of feedback loops and they interact. So if you can imagine that somebody else spread the opposite rumor, somewhere else in the system, then these two circulating rumors may hit each other somewhere. And they will feed back to a way. and to the other person. So possibly A will change his mind about the rumour or not.

So there's immense combinatorial complexity to these networks and the loops. And that's one of the reasons that systems which locally are easy to understand, it's easy to understand somebody's telling a rumour to somebody else, that when you look across the whole network, it gets very complicated. And then, just to bring back to a sort of base route, for which the programme began with Ian's comments, you're trying to work this out with mathematical formula. Well, with a combination of mathematical formula and computation,

so that in traditional science you would have a formula, for example, with Newtonian physics, so that if you fire a cannonball, you can predict exactly where it's going to land and exactly when it's going to land. In most of the systems that we call complex, you can't do that with that degree of certainty. So very often the best you can do

is to know what the possible outcomes will be of any particular action. The notion of equilibrium which you brought up, would you like to develop that a little? That's another word that's in play inside this theory. These are perfectly ordinary words, but they mean something else in the theory that you're developing. It does, very much so. And actually, if I may start by referring back to feedback,

to what Geoffrey just explained. Because again, we need to distinguish between, two kinds of feedback, positive and negative feedback. And in positive feedback, which is what Jeffrey has discussed, there could be multiple equilibria.

Now we need to distinguish that from negative feedback. Let me give you an example of negative feedback, because negative feedback is associated with a mechanistic system. So a central heating system is based on negative feedback.

So the temperature drops, it is, you feel colder than you would like. The thermostat will then switch itself on. It will raise the temperature to the desired one. So it closes the gap between the actual and the desired. And that has a single equilibrium point. Now, the point here is that we assume a single equilibrium point in complex systems like the economy, and we make wrong assumptions. So, for example, we assume that as in a simple mechanistic system with a single equilibrium point, if we apply the right amount of correction at the correct time, which we can do with something like a central heating system, it will actually go back to its equilibrium.

Now, we cannot do that with things like the economy which is complex. So let me now explore that further. We've got to get a move on, but still, that's fine. Explore it a bit further, but let's go. No, no. I'll go back to the idea of far from equilibrium, because I think that's what you were asking me. And I was asking about, we're getting there.

We're getting there. Okay. In this idea of far from equilibrium, it is the idea that you cannot go back to what existed in the past. It is not re-establishing a position because the system, by exploring new alternatives and evolving and co-evolving, it will actually attain a different state. So you've got a shifting equilibrium. If things change the equilibrium, the position of that equilibrium shifts with a shift with a change. It shifts, but there also, there could be multiple equilibrium at the same time, not a single one. Yeah.

That is the key thing here. Yep, I've got that. Or indeed, there may be no equilibrium at all. Yes, exactly. But the system might be in a state of constant change. Yes. Well, we know where we are with equilibrium, Manny. Yes, I think so.

Right. Now we're going to go to emergence. these common or garden words assume plungeant dark significance right emergence this is the biggie this is the really interesting

phenomenon and it's when the system does things on the system scale which you would not be able to predict from the components and the way they interact so let's take the human brain

it's a complex system the entities are neurons nerve cells, they are connected to each other, they send signals to each other. They're all very simple. They're all very simple, and in fact you can write down mathematical equations which are quite good representations of what neurons do.

But now you connect a huge lot of them together. Billions. And out of this come things like consciousness. We're actually aware of ourselves and our surroundings in this rather vivid way. There is nothing in the structure of a neuron that says it's got to do that. in a sense the neurons don't know about that

and yet certainly cognitive scientists would say this is not some extra external thing that has wonderfully been imposed by some supernatural element So your complex system is trying to track that this happens or why it happens

or the consequences of it happening? There are, this is back to what Eve was saying about structures structures that appear which are new kinds of things. Think of the weather Now let's think of the brain. It's much more interesting than the weather. Well, think of the brain.

Because everyone, let's go with weather just to noise people. But the brain's interesting. You can understand little bits of the brain. And actually those are quite difficult. I've spent years working on models of very tiny bits of, you know, how do animals move? What sort of signals go to the legs? You've only got four legs if it's an animal.

It's, you know, this is not as complicated as the whole brain. But all of the evidence is that somehow, All of the wonderful things the brain does, like language, like vision, hearing, taste, our senses, our movement. All of this happens by neurons exchanging electrical and chemical signals along a network. The network changes as we learn. It changes as we grow from babies to adults. So as a mathematician, your task is to track this complexity inside the brain. In a sense, it's to try and find out.

what's happening, not exactly despite the complexity, but the complexity is what makes it work, but what it does may not be as complex in itself as all of the underlying details. When I'm talking to you, we could describe the whole conversation in ordinary language, very, very clearly in a sense the conversation does that. If I tried to find out and write down

what all of the nerve cells in our brains were doing when that happened, it would be impossible to describe. Jeff, you want to come in. Yeah, this brings us to what I think is a very important area. Can we keep the notion of emergence? Well, indeed. I'm going to say in multi-level systems, so in this particular case you've got,

at the micro-level you've got the neurons, and at some macro-level you've got the brain itself, where you've got different behaviours. And in science, we have theories at micro-levels and at macro-levels, and very often these don't tie together. And to say something interesting about brains, actually, At a level above that, of course, we have social intelligence where we combine our brains and what our brains are doing

to have something which is different. It's not the individual level of intelligence, but the social intelligence. Such as? Well, the social intelligence would be something like a political... thing like the House of Parliament, for example. You've got 600 MPs making a collective decision, which is different from what any one of them might have done alone. I know you, but can you come in, there's this,

so do you want to say first and ask you a question, right? Okay, I just wanted to go a little bit, a step further from what Ian and Geoffrey said, because in terms of emergence, they have described in a way a bottom-up process that arises from interaction of the different entities interacting. So we get the emergent in, you described consciousness as an emergent property, which is qualitatively different from the individual neurons. Now, once that emergent is in place, there is an additional dynamic because the emergent has two effects.

It both constrains certain behaviours of the interacting entity. Because there's a system in place? Yes. While at the same time, it opens up new possibilities. And that makes it a very, very dynamic process. So it's not only a bottom-up process, it's also a top-down process, and the whole thing is changing very dynamically all the time. So we can go back to the Arab Spring as a simple example of that.

It emerges. And it's looking to ape the previous equilibrium, but it's changing all the time. And as you said, there are several points of equilibrium there as well. Jeff. I'd say in that particular case that there's a notion of latency, so that very often systems in a state where things are predisposed to happen but might not happen.

And so although it's unpredictable, there may be some expectation that there will be some outcome. The bottom-up phrase is useful, Ian, is it? Yes, I think so. I mean, bottom-up, top-down, they capture a certain amount of this because the way we model these complex systems,

certainly mathematically, is essentially bottom-up. Can you just be even more precise about that? Okay, understand the components of the system, find out the rules for how they interact. So if I'm talking about people moving in a building, forming a crowd, we want to know how individuals behave

in terms of where they are in the building and the other people around them. And actually the rules for people moving in buildings in practice are pretty straightforward. You know where you want to go. If there's a gap in that direction, you move into that gap, but you don't bump into other people.

And I've almost summarised the rules you need. Put those together and you get quite really models of how crowds flow through buildings. Yeah, but the models sometimes don't work. Hillsborough didn't work. That was a crowd. Well, no, that was the wrong model. Hillsborough, they had an old-fashioned style equilibrium model.

They thought the crowd was like a fluid, and it would simply, if there were too many people in one place, they would flow into the places where there were gaps. Now, a real crowd is not like that, and a complex system model of a crowd doesn't do that. Jeff, you want to come in. Yes, I was going to give you another example of bottom-up emergence that, for example, people come together and make Facebook groups,

and that's another example of social intelligence. Right. Can you tell us in which areas, in my introduction, or in the trail, I can't remember now, I talked about this applying to ants and to starlings as well as to the stocker. In which areas has most progress been made so far that really getting, you think you've got a grip on it, and why is that? Can we talk about that? Do you want to start?

Yes. I would say that complex system science will apply to all disciplines, so that the notion that you have systems which are, say, sociological or geographical or physical or whatever, this is kind of characteristic of the old science, that the science of complex systems is interdisciplinary and multidisciplinary. And so this science is applying, for example, in medicine, in so-called personalised medicine, where instead of you getting a treatment which will, applied to the average person, it actually fits you personally.

The same is potentially true in education. We've mentioned transportation, road systems, etc., being analyzed with this kind of science epidemics. I think it's going to apply to actually everything. Eve and Kelly, we use computers to do millions and millions of calculations increasingly into the billions now. Is there any other way of getting at the understanding of this, or is that the only way crashing through,

bigger and bigger computers. No, no, no. I'm glad you've asked me that question. No, there is the on the qualitative side, when we try to understand the behaviour of humans, we do need to actually talk to them. And therefore, we

need to use tools and methods that social scientists use. So, for example, if we want to understand epidemics and even worse, pandemics, it isn't enough to only understand the epidemiology.

We also need to understand how different agencies will interact during an outbreak. So we need to actually, and the consequence of, we need to also look at, for example, how will the infrastructure be affected in terms of the water, the food, security, etc., etc. And therefore, we need to look at the whole picture and all. those organizations, institutions that interact. We cannot do that by using computers alone. We actually need to understand why. Why do people interact in the way they do?

Why would they do something under particular circumstances? And to understand those whys, we actually need to use more qualitative methods. So why is an emergent thing? they behave differently than they would as individuals. Sorry, can you repeat that? In the sense of emergence that you've been talking about, where the idea is that when people come together, it emerges, they will behave as they would not have behaved as individuals.

Okay. Let's make a distinction between patterns and individuals. For example, when we're looking at evacuation after a major disaster, we can predict certain patterns of behavior. But in no way can we predict how individuals, will actually behave and react. You can't predict the details of each individual, but there are these large scale.

It's not exactly statistical, but it's like statistics. There are regularities in the behaviour of humanity in large groups, independently of the people. That behaviour emerges from what the individuals do, and if you track that in detail, it would be extraordinarily complicated. But actually what you get is a wave of 100,000 people evacuating a city and they're all going down the roads because where else would they go? Can I just stay with you, Ian, and talk.

He referred to medicine and progress made in medicine. Can you tell us what's gone on there and how this theory is already making inroads into understanding how things move around and develop? Yeah, the traditional models, as Jeff was saying, aren't modelling the system on the right level in the right kind of way. The complex system models of an epidemic, actually you can build into those models all sorts of real-world behaviour, such as people getting onto an aeroplane and flying to another country.

And you would do this not in terms of what individuals really do. You don't have a particular person in your model, but you have a representative set of entities which are the right number of people are flying in the right direction. And you can then model the spread of the epidemic with some degree of accuracy, whereas the old models would tend to say, well, if there's an outbreak in China,

the first thing it will do is spread all the way through China at a particular speed, and then when it gets to the borders, it will spill over into neighbouring country. It's not like that. Somebody gets on a plane, and suddenly there's a new outbreak starts somewhere else. You can cope with that kind of.

kind of structure. Jeff. Jeff Johnson. I think we should make it very clear that these computer-based investigations of the future, they're not predictions, so you don't run the system once and get the answer.

What happens is that you have to run the system many times because most of these systems are sensitive to initial conditions. So through the computer simulation, you get an understanding of the space of possibilities and that's what you need to use for policy purposes and for making decisions.

But initial conditions have their own dynamics. as well, don't they? If the initial condition when you set up a typewriting system is called QWERTY, although it isn't the most sensible, logical, it sticks because that's the one and you get, so there's a different sort of factor coming in there. Well, that's the classic example of so-called path dependence

which is that what happens in a system will, depends on its history so that the evolution of the typewriter came for that reason. It's also positive feedback in your sense. The reason you use a QWERTY keyboard is because everybody uses a QWERTY keyboard. Yes.

I'm sometimes when you're talking, getting the impression there's so much you're taking to account. I don't see how you're going to arrive at where you're setting out to get to. Eve, you're waving away now. Let's hope we have the answer. Okay. You asked earlier the question, you know, what kind of problems can we deal with? And whether we have to actually look at all the detail. No, it's not the detail that, the tiny detail that we need to look at, is we need to understand a complex problem.

problem in a way that we can actually address it. Well, to take a large organisation, which is complex, and inside large organisations are often other organisations, subservient to it, which are also complex. Inside those are, it is Russian boxes, isn't it? It is Russian boxes. And let me give you an example, because at the moment we're working with a government agency in Indonesia

that is facing deforestation. So for example, here, the problem is very complex, is very large. And what we are trying to do is to find out what are the, first of all, the different dimensions, the social, the culture, the political, the economic, the technical, the physical, in which that problem exists. Because if we understand that, but not only as laundry lists, but how the issues within those dimensions interact and influence and change each other. Are you approaching the level of, at the moment, of impossible to understand?

By the time you get all this together, and you've got this vast population in Indonesia, and each of those might have a mind of their own. No? No. I'm talking about one organisation here. This is a government agency, and we're looking at the problem they are facing. And no, it is not an endless number.

It is actually identifying some key clusters of issues. I'd like to emphasize the fact that we call it complex systems doesn't mean that this is some kind of thing that only very small number of people can understand that in fact most people understand complexity and handle complexity extremely well and so complexity is ordinary the thing about complexity sciences as we said at the beginning it's a different way of thinking and as you said the science is quite young so we don't have answers for everything and it would be disingenuous if we said we did. But I think that in the scientific community there is quite a coherent view

of the kind of things we've been talking about today. There's certainly a very long way to go. But I think that this is a science which is accessible to everybody. Eve. I think that is absolutely correct. It is how do we understand complex systems? If we understand the characteristics of complex systems

we can work with those characteristics. If we don't understand them, we can actually inadvertently block them and go against what we want to achieve. So it is a way of thinking and it is a way of understanding the reality of the world. Can I find to come to you against you?

Where are we at the moment with Complex Syria? How far down the track are you? And what's it best at? It's got to the point where we have quite a lot of examples of models some of which work pretty well. Crowd modelling, for example, is now established as a commercial tool. It's used all the time.

And we have some sort of theoretical understanding of some of the issues we've been discussing. It may have sounded a bit vague, but that's actually because it's a very, very broad area. And I think we can see directions in which progress can be made. But it is very much early days at the moment. There's a lot of work going on. Thanks for giving us an early glimpse of what was going to sweep the 21st century of its feet. Thank you, Eve Middleton, Kelly and Stuart, Jeff Johnson. And next week we'll be talking about the Medici,

the family who dominated Florence's political and cultural life for three centuries. Thanks for listening.