Simply Complexity (3 page)

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.

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 trying to predict whether the bar will be over-capacity or not, and hence what your action should be. Everyone else is trying to do the same. So this is again an ideal candidate Complex System since it comprises a collection of objects (bar-goers) competing for a limited resource (a place in the bar).

Say you decide not to go. Instead you will cook a nice meal at home. But you need to buy food. Where should you go? There are two supermarkets, one called “zero” and the other called “one”, on opposite sides of the town. Which will be least crowded? It is again the same situation of competition for a limited resource – in this case, space in the market.

Things don’t get better when, following the meal, you decide to go online and review the stock that you bought a year ago. You
get the price chart up on your screen. The stock’s price has gone up and down – but what is that telling you? Should you buy more stock, or sell the stock you already have? Suppose you decide to sell. If everyone else also decides to sell, there will be a sudden oversupply of these shares. Nobody would then pay you very much for them. On the other hand if you manage to sell at a moment when there are lots of buyers, you will be laughing. The same holds for selling things on any other market, from housing through to eBay. Even though you may be buying or selling based on some long-term preference or need, the decision of exactly when to buy or sell is a strategic one – and is dominated by the need to predict what everyone else will do. In other words, you must once again try to out-guess the crowd. Everybody else is again trying to do the same, and obviously not everybody can win. As a result, we once more have an ideal candidate system for Complexity since we have a collection of objects (investors) competing for a limited resource (a favorable price).

When you start to think about it, there are loads of examples from our everyday lives where, in one form or another, we are indirectly trying to out-guess what everyone else will do. And unfortunately for all of us, the correct action in such situations is determined by what everybody else actually does. What is worse is that such everyday problems are repeated over and over again, as each day goes past. This then tempts us to try to learn from the past and hence adapt our strategies to try to improve our chances of coming out on top. In other words, our daily life becomes a sequence of ongoing games – a sort of multiple “rat race”.

This common everyday situation in which a collection of objects (people) repeatedly compete for some kind of limited resource, illustrates the complexities of everyday life extremely well – a fact that was first pointed out by Brian Arthur and later by John Casti, both of the Santa Fe Institute in New Mexico. But even more remarkable is the fact that it also provides us with a generic Complex System which can be adapted to describe a wide range of scientific, medical, and technological scenarios. We have already discussed various applications in section 1.2 in connection with the design of collections of machines – and as we move further
through the book, we will see this same generic set-up reappearing in various guises.

There is no rigorous definition of Complexity. But that isn’t so bad – after all, it is hard to define a word such as “happiness” and yet we all know what its characteristics are. We will characterize Complexity in a similar way by describing the features which a Complex System should have, and looking at the behaviors which it should then show. This might sound very abstract – but fortunately the everyday scenarios that we have discussed come straight to our rescue. Indeed it will turn out that these characteristics are the very same ones that make our own everyday lives so complex.

Most Complexity researchers would agree that any candidate Complex System should have most or all of the following ingredients:

The system contains a collection of many interacting objects or “agents”.
In the case of markets, these are traders or investors. In the case of traffic, these are drivers. Typically the scientific community refers to such objects as agents. Interactions between these agents may arise because the agents are physically close to each other, or because they are members of some sort of group, or because they share some common information. For example, the agents may be linked together by some public information that they share – like investors who are watching the same price chart for a given stock, or commuters who are listening to the same traffic report on the radio. On the other hand, some agents may be linked together by private information, like two investors who happen to be friends sharing private information over the phone. To the extent that the agents are linked together through their interactions, they can also be thought of as forming part of a network. For this reason, networks have become an integral part of Complexity Science, together with the study of collections of agents. Indeed for many scientists in the community, the study of Complexity is synonymous with the study of agents and networks together.

These objects’ behavior is affected by memory or “feedback”.
This means that something from the past affects something in the present, or that something going on at one location affects what is happening at another – in other words, a sort of knock-on effect. For example, if you happened to have taken Route 0 home for the past few nights and it was always overcrowded, you may choose to flip to Route 1 tonight. Hence you have used information from the past to influence your decision in the present – in other words, the past has been fed back into your present decision. Of course the nature of this feedback can change with time. For example, you may care less about past outcomes if it is the start of the week as opposed to the end of it. The net result of everyone having such memory can be that the system as a whole also remembers. In other words, a particular global pattern or sequence appears in the traffic or in the stock market.