Simply Complexity

A Clear Guide to Complexity Theory

Neil Johnson

• Publisher: Oneworld Publications
• Year: 2009
• eBook ISBN: 9781780740492
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

The new branch of science which will reveal how to avoid the rush hour, overcome cancer, and find the perfect date What do traffic jams, stock market crashes, and wars have in common? They are all explained using complexity, an unsolved puzzle that many researchers believe is the key to predicting - and ultimately solving - everything from terrorist attacks and pandemic viruses right down to rush hour traffic congestion. Complexity is considered by many to be the single most important scientific development since general relativity and promises to make sense of no less than the very heart of the Universe. Using it, scientists can find order emerging from seemingly random interactions of all kinds, from something as simple as flipping coins through to more challenging problems such as predicting shopping habits, the patterns in modern jazz, and the growth of cancer tumours.

PART 1

 

What exactly is Complexity Science?

Chapter 1

Two’s Company, Three is Complexity

1.1 A definition, of sorts

Take a look in many dictionaries, and you will find Complexity defined along the lines of “The behavior shown by a Complex System”. Then look up “Complex System”, and you will probably see “A system whose behavior exhibits Complexity”. So what’s going on? Well, unfortunately, Complexity is not easy to define. Worse still, it can mean different things to different people. Even among scientists, there is no unique definition of Complexity. Instead, the scientific notion of Complexity – and hence of a Complex System – has traditionally been conveyed using particular examples of real-world systems which scientists believe to be complex.

This book will take the “complex” out of Complexity, by going to the heart of what connects together all real-world Complex Systems. We will uncover the magic ingredients which make something complex as opposed to just being complicated, and show how Complexity is deeply engrained in our own everyday lives. We will also see why Complexity is set to revolutionize our understanding of science, and help resolve some of the most challenging problems facing society as a whole.

Complexity can be summed up by the phrase “Two’s company, three is a crowd”. In other words, Complexity Science can be seen as the study of the phenomena which emerge from a collection of interacting objects – and a crowd is a perfect example of such an emergent phenomenon, since it is a phenomenon which emerges from a collection of interacting people. We only have to look at world history to realize that it is riddled with major events which have been driven by human crowd behavior. Everyday examples of crowds include collections of commuters, financial market traders, human cells, or insurgents – and the associated crowd-like phenomena which emerge are traffic jams, market crashes, cancer tumors, and guerilla wars. Even extreme weather conditions such as floods, heatwaves, hurricanes, and droughts can be seen as a sort of crowd effect, since they emerge from the collective behavior of “packets” of water and air in the form of oceans, clouds, winds and air moisture. And if we add to this the collective actions of humans – in particular, the environmental changes caused by human activity – we conjure up the controversial emergent phenomenon known as “global warming”.

1.2 Complexity in action

At the heart of most real-world examples of Complexity, is the situation in which a collection of objects are competing for some kind of limited resource – for example, food, space, energy, power, or wealth. In such situations, the emergence of a crowd can have very important practical consequences. For example, in a financial market, or the housing market, the spontaneous formation of a crowd of people who wish to sell – and hence are effectively competing for buyers – can lead to a market crash in which the price falls dramatically in a short time. A related crowd phenomenon occurs among commuters who are competing for space on a particular road at the same time. This leads to a traffic jam, which is the traffic equivalent of a market crash. Other examples include Internet overloads and power blackouts, in which subscribers simultaneously decide to access and hence exhaust the available resources of a particular computer system or power network. Even wars and terrorism can be viewed as the collective, violent actions of different groups of people who are fighting for control of the same resources, e.g. land or political power.

The Holy Grail of Complexity Science is to understand, predict and control such emergent phenomena – in particular, potentially catastrophic crowd-like effects such as market crashes, traffic jams, epidemics, illnesses such as cancer, human conflicts, and environmental change. Are they predictable in any way, or do they just appear out of nowhere without warning? Can they be controlled, manipulated or even avoided?

What is remarkable about such emergent phenomena, is that they can arise in the absence of any central controller or coordinator. Just think about the level of coordination and communication which some central controller would actually require in order to be able to recreate a particular traffic jam. In other words, imagine the number of cell-phone calls he would have to make to ensure that all the drivers were on the same road at the same time, and in one particular pattern. It simply couldn’t be done in a reliable way. This represents a universal feature of Complex Systems: emergent phenomena can arise without the need for an “invisible hand”. Instead, the collection of objects is able to self-organize itself in such a way that the phenomenon appears all by itself – as if by magic.

The sheer power and momentum of these emergent phenomena can also be quite remarkable. We all know how easy it is to be swept up in the ebbs and flows of mob mentality – whether intentionally or unintentionally. Recent decades such as the 1970s delivered cultural tsunamis in terms of fashions and hairstyles: just think flared trousers and platform shoes. In the 1990s, we had the infamous dot-com boom with company employees agreeing to be paid in stock options rather than hard cash – only to find themselves penniless when the bubble burst around April 2000. And who hasn’t had the experience of wandering along a busy street in the middle of a crowd of people, only to find yourself separated from your companions and going in a direction you don’t actually want to go? We each seem to have an innate urge to join in with a crowd – but it may not be the best decision from our individual perspective. Just think of selling or buying a house or car. You will get a far better price if you sell when everybody else is buying, and vice versa.

It is not just collections of people that show emergent phenomena. The animal, insect and fish kingdoms are awash with examples of self-organization: from ant-trails and wasp swarms through to bird flocks and fish schools. In fact, biology is sitting on a treasure-chest of such collective phenomena – from the immune system’s collective response to invading viruses through to intercellular communication and signalling which drives many important biological processes. The fact that all these effects represent emergent phenomena explains why so many different disciplines are getting interested in Complexity.

Closer to everyone’s personal concerns – and indeed, worries – is the area of human health and medicine. This is a prime example of Complexity in action. Our immune system consists of a collection of defense mechanisms for dealing with invading viruses. However just like the traffic, the stock market and the Internet, the system can go wrong all by itself – for example, when the collective response of the immune system ends up attacking healthy tissue. Hence understanding the extent to which we can predict, manage and even control a Complex System has particular importance from the perspective of human health. Indeed it may even lead to new forms of treatment whereby the collective responses of the body are harnessed to deal with a specific problem in a particular organ, rather than relying on one particular targeted therapy. A cancer tumor is a particularly horrific example of a crowd effect gone wrong. Instead of staying in check, cells begin to multiply uncontrollably – and just as with other Complex System phenomena such as traffic jams, it becomes very hard to know what to do to reduce the size of the tumor without causing some even more damaging secondary effects. For example, any treatment which involves damaging the tumor may indirectly lead to the survival of the fittest, most malignant cells.

Interest in Complexity is not confined to natural objects such as people, animals or cells. The ability of a collection of objects to produce emergent phenomena without the need for some central controller, has attracted the attention of researchers at NASA. In particular, Kagan Tumer and David Wolpert have been leading a research team at Ames Research Laboratory in Mountain View, California which is looking at emergent phenomena in collections of machines. The machines in question could be robots, satellites, or even micro-spacecraft. For example, NASA are investigating the possibility that a collection of relatively simple robots can be used to explore the surface of a planet in a fast and efficient manner – as opposed to using one large and far more complicated machine. They have a good reason for doing this. If one robot in this collection were to malfunction, there would still be plenty more available. By contrast, a single malfunction in the large machine could lead to the immediate termination of a very costly mission. This also explains NASA’s interest in exploring the properties of collections of simple satellites, as opposed to one large sophisticated one – and also collections of micro-spacecraft as opposed to one much larger one.

But there is another, far more intriguing reason that NASA is interested in such research. Most NASA missions are likely to involve sending machines to distant planets – and it is hard to maintain reliable communication channels over such distances. It would therefore be wonderful if NASA engineers could just sit back, relax and let the machines on the planet sort it out for themselves. This would of course land the machines with the same difficulty as we have when trying to arrange a lunch-date by phone with a group of friends. Judging from what typically happens with the lunch-date problem, you might think that one of the machines would simply end up acting as the local coordinator, checking oneby-one the position and availability of each machine and then coordinating their actions. This sounds like it should work fine – however, the collection of machines would then be reduced to having the same vulnerability as a single sophisticated machine. If the local coordinator malfunctions, the mission is once again over. Instead, the “killer application” aspect of such a collection of machines, and hence the interest in such Complex Systems within NASA, is that it is not necessary for the machines to have local coordination in order for them to do a good job. It turns out that a suitably chosen collection of such objects can work better as a group if they are not being coordinated by some single controller, but are instead competing for some limited resource – which is actually NASA’s case, since there will typically be relatively few loose rocks available for picking up within a given area of a planet’s surface.

A busy shopping mall provides a nice everyday example of why such a collection of selfish machines could be so useful. Imagine that you have dropped a one-hundred dollar bill. You organize a search-team, stating that they will all share the money when it is found. If the search-team is a large one, you will have great difficulty in coordinating everybody’s actions – hence you might never find the money. By contrast, if you tell everyone that the money is theirs if they find it, their individual selfish drive will likely be so strong that the money is found very quickly. In the sense that dropped bills are like available rocks, we can see that the collective action of selfish machines could be used to solve quite a complicated search problem.

There are even research groups investigating how such a collection of machines might design itself, by allowing the individual machines to adapt and evolve of their own accord. This research borrows ideas from real-world situations involving collections of humans. After all, humans acting in the setting of a financial market are doing nothing other than competing for a limited resource in a selfish way – exactly like the machines. The same applies for drivers in traffic: it is because of their competition for space on a road that we typically see arrangements of cars which are spread out in some reasonably regular pattern.

Now, if you are reading this book on a plane, you might want to take a deep breath. The increasingly high-tech nature of on-board computer systems means that each next-generation aircraft will itself be a Complex System – a Complex System which needs to be managed and controlled. But as well as creating a challenge in itself, ideas from Complexity are being harnessed to develop novel designs for such aircraft. For example, Ilan Kroo and co-workers at Stanford University have been looking at lining the back of conventional aircraft wings with a collection of robotic microflaps. The design is such that the flaps compete to be orientated in the right direction at the right time, according to the plane’s planned trajectory – just like our selfish shoppers would compete to be in the right place at the right time in order to pick up the lost money. A central controller, which in this context is an aircraft pilot, would therefore no longer be needed. Now, the possibility of pilot-less planes might sound scary, but apparently many people would indeed be willing to fly in such an aircraft as long as it is cheap – and as long as their bags turn up on time.

And while we are in the air, what about those air conditions? More generally, what about the effects of our own collective actions on our environment and weather? Global competition for increasingly scarce natural resources is leading to increased levels of pollution and deforestation, and these may in turn affect our climate. The weather results from a complicated ongoing interaction between the atmosphere and oceans, connected as they are by currents of water, winds and air moisture. Floods, hurricanes, and droughts represent extreme phenomena which emerge from this collective behavior. Although scientists know the mathematics which describes individual air and water molecules, building up a picture of what billions of them will do when mixed together around the globe is extremely complicated. Now add on top of this the collective actions of human beings, and you come up against the emergent monster of global warming – and in particular, the complex question of evaluating how the Earth’s climate is affected by the collective actions of its inhabitants, and what can then be done about it.

So that is Complexity in action – from technology, to health, to everyday life. But does it play any role in fundamental science, and in particular fundamental Physics? Well, it turns out that it does – and in a very big way. When you get down to the level of atoms, the range of emergent phenomena is simply breathtaking. Electrons are negatively charged particles which typically orbit the nucleus in an atom. However if you put together a large collection of such electrons, you will uncover a wealth of exotic crowd effects: from superconductivity through to effects such as the so-called Fractional Quantum Hall Effect and Quantum Phase Transitions.

It doesn’t stop there. If we take just two particles such as electrons, they can show a particular type of “quantum crowd effect” called entanglement. This is an emergent phenomenon which is so bizarre that it kept Einstein baffled for the whole of his life. Indeed the information processing power underlying such a quantum crowd is so powerful that it has led to proposals for a quantum computer, which is a fundamentally new type of computer that is light years ahead of any conventional PC; quantum cryptography, which can yield completely secure secret codes; and quantum teleportation. There is even the possibility that such effects are already being exploited by Mother Nature herself – but more of that in chapter 11.

Even the fundamental physics of Einstein’s space–time and Black Holes doesn’t escape the hidden clutches of Complexity. At the very heart of Einstein’s theories of relativity was the idea that space and time are coupled together. Another way of saying the same thing is that two pieces of space and time can interact with each other by means of light passing between the two. Hence the entire fabric of space–time is a complicated network of interconnected pieces. In chapter 5 we will look more closely at networks in general – suffice to say that they are just another way of representing a set of objects that are interacting, i.e. they are just another way of representing a Complex System.

In all of these examples, the precise nature of the crowd-like phenomena which emerge will depend on how the individual objects interact and how interconnected they are. It is extremely difficult, if not impossible, to deduce the nature of these emergent phenomena based solely on the properties of an individual object. For this reason, it is pretty much true that every new crowd effect which is found involving fundamental quantum particles such as electrons, leads to a Nobel Prize in Physics. Even though we understand the properties of a single electron, for example, the corresponding emergent phenomena from a collection of them tend to be so surprising that each one represents a remarkable new discovery by itself. On an everyday level, we know that market crashes and traffic jams can also be surprising – both in their form and in terms of when they occur and how long they last. Given this difficulty in predicting what crowd effects will arise, under what conditions and when, we can begin to see how Complexity Science might also be referred to as the science behind surprise.

So it seems like Complexity has many possible applications across the sciences, medicine and in our everyday world. Whether you are interested in fundamental physics, biology, human health, or you just want to avoid traffic jams on your way home from work, Complexity is key.

1.3 Why is my own life so complex?

It is 6 p.m. You are leaving work – and the only thing on your mind is to get home quickly. But which route should you take? It turns out you have a choice. But so does everybody else. And this is the point: the best route is the one which is the least crowded – but it is the collective decisions of everyone else which determine which of the possible routes this turns out to be. In effect you are not deciding between routes home – you are instead trying to out-guess everyone else. In other words, you are trying to out-guess the crowd in the competition for space on the road. Of course, everyone else is trying to do the same. Thinking back to our earlier discussion, this everyday situation represents an ideal candidate Complex System since it comprises a collection of objects (drivers) competing for a limited resource (road space).

But your complex life doesn’t stop there. You get home, eventually, and decide you would like to go out to relax. You want to go to a particular bar – but let’s assume that this bar has a limited capacity and so not everyone who turns up may actually get in. You yet again find yourself having to decide which choice to make: do you make the effort to get ready, get to the bar and run the risk that you won’t get in? Or do you stay at home and run the risk that you are missing a great night out? Since the bar has a limited capacity, and yet is so popular that there are lots of potential attendees, you are again trying to out-guess the crowd. In particular, you are try...

Table of contents

• Cover
• Title Page
• Copyright
• Contents
• Preface
• Part 1: What exactly is Complexity Science?
• Chapter 1: Two’s Company, Three is Complexity
• Chapter 2: Disorder rules, OK?
• Chapter 3: Chaos and all that jazz
• Chapter 4: Mob mentality
• Chapter 5: Getting connected
• Chapter 6: Forecasting financial markets
• Chapter 7: Tackling traffic networks and climbing the corporate ladder
• Chapter 8: Looking for Mr./Ms. Right
• Chapter 9: Coping with conflict: Next-generation wars and global terrorism
• Chapter 10: Catching a cold, avoiding super-flu and curing cancer
• Chapter 11: The Mother of all Complexities: Our nanoscale quantum world
• Chapter 12: To infinity and beyond
• Appendix: Further Information
• Index